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Math Problems
Algebra 2
Characteristics of quadratic functions: equations
Try
9
9
9
\newline
Explain why the graph of
y
=
x
2
−
2
x
+
2
−
p
y=x^{2}-2 x+2-p
y
=
x
2
−
2
x
+
2
−
p
, where
p
>
1
p>1
p
>
1
, intersects the
x
x
x
-axis at two points.
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Find the
y
y
y
-intercept of the parabola
\newline
y
=
x
2
+
4
x
+
37
4
.
y=x^{2}+4 x+\frac{37}{4} \text {. }
y
=
x
2
+
4
x
+
4
37
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
□
\square
□
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What is the maximum vertical distance between the parabola
y
=
3
−
x
2
y=3-x^{2}
y
=
3
−
x
2
and the line
y
=
x
+
1
y=x+1
y
=
x
+
1
for
−
2
≤
x
≤
1
-2 \leq x \leq 1
−
2
≤
x
≤
1
?
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Problem
25
25
25
.
10
10
10
\newline
For the function
f
(
x
)
=
x
2
−
6
x
+
9
f(x)=x^{2}-6 x+9
f
(
x
)
=
x
2
−
6
x
+
9
\newline
Determine the coordinates of the
x
x
x
-intercepts.
\newline
Determine the coordinates of the
y
y
y
-intercept.
\newline
Determine the equation of the axis of symmetry.
\newline
Determine the coordinates of the vertex.
\newline
Sketch a graph of the function, label the
x
x
x
and
y
y
y
axes with an appropriate scale
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The equation of a line is
y
+
4
=
6
x
+
13
y+4=6 x+13
y
+
4
=
6
x
+
13
\newline
What is the value of
y
y
y
at the point where the line crosses the
y
y
y
-axis?
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The parabola
y
=
x
2
y=x^2
y
=
x
2
is scaled vertically by a factor of
7
7
7
. What is the equation of the new parabola?
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Find the
y
y
y
-intercept of the parabola
y
=
x
2
+
17
4
y = x^2 + \frac{17}{4}
y
=
x
2
+
4
17
. Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
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Find the
y
y
y
-intercept of the parabola
y
=
x
2
+
7
y = x^2 + 7
y
=
x
2
+
7
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
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Find the equation of the axis of symmetry for the parabola
y
=
x
2
−
19
2
y = x^2 - \frac{19}{2}
y
=
x
2
−
2
19
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
\_\_
__
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
−
x
−
8
y = x^2 - x - 8
y
=
x
2
−
x
−
8
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
_
_
_
\_\_\_\_\_
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
+
6
x
+
71
10
y = x^2 + 6x + \frac{71}{10}
y
=
x
2
+
6
x
+
10
71
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
\_\_
__
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
−
4
x
+
1
y = x^2 - 4x + 1
y
=
x
2
−
4
x
+
1
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
\_\_
__
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
−
7
x
+
3
y = x^2 - 7x + 3
y
=
x
2
−
7
x
+
3
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
\_\_
__
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
−
5
x
+
9
y = x^2 - 5x + 9
y
=
x
2
−
5
x
+
9
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
\_\_
__
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
+
5
x
+
19
2
y = x^2 + 5x + \frac{19}{2}
y
=
x
2
+
5
x
+
2
19
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
+
3
y = x^2 + 3
y
=
x
2
+
3
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
_
_
_
\_\_\_\_\_
_____
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
+
5
x
+
10
y = x^2 + 5x + 10
y
=
x
2
+
5
x
+
10
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
−
4
x
+
13
5
y = x^2 - 4x + \frac{13}{5}
y
=
x
2
−
4
x
+
5
13
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
+
6
x
y = x^2 + 6x
y
=
x
2
+
6
x
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
_
_
_
\_\_\_\_\_
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
+
x
+
2
y = x^2 + x + 2
y
=
x
2
+
x
+
2
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
_
_
_
\_\_\_\_\_
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
+
37
10
y = x^2 + \frac{37}{10}
y
=
x
2
+
10
37
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_____
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
+
2
x
+
6
y = x^2 + 2x + 6
y
=
x
2
+
2
x
+
6
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
+
5
y = x^2 + 5
y
=
x
2
+
5
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
+
2
x
+
9
5
y = x^2 + 2x + \frac{9}{5}
y
=
x
2
+
2
x
+
5
9
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
−
4
x
−
2
y = x^2 - 4x - 2
y
=
x
2
−
4
x
−
2
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
+
9
y = x^2 + 9
y
=
x
2
+
9
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
_
_
_
\_\_\_\_\_
_____
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
+
7
x
+
6
y = x^2 + 7x + 6
y
=
x
2
+
7
x
+
6
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
−
7
y = x^2 - 7
y
=
x
2
−
7
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_
_
\_\_
__
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
−
6
x
+
7
y = x^2 - 6x + 7
y
=
x
2
−
6
x
+
7
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
+
6
x
+
9
y = x^2 + 6x + 9
y
=
x
2
+
6
x
+
9
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
_
_
_
\_\_\_\_\_
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
+
61
10
y = x^2 + \frac{61}{10}
y
=
x
2
+
10
61
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
\_\_
__
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
+
x
y = x^2 + x
y
=
x
2
+
x
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
_
_
_
\_\_\_\_\_
_____
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
−
19
2
y = x^2 - \frac{19}{2}
y
=
x
2
−
2
19
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
−
x
−
8
y = x^2 - x - 8
y
=
x
2
−
x
−
8
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
−
9
y = x^2 - 9
y
=
x
2
−
9
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
−
7
x
+
9
y = x^2 - 7x + 9
y
=
x
2
−
7
x
+
9
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
+
11
2
y = x^2 + \frac{11}{2}
y
=
x
2
+
2
11
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
\_\_
__
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
+
1
y = x^2 + 1
y
=
x
2
+
1
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
\_\_
__
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
−
4
x
+
5
y = x^2 - 4x + 5
y
=
x
2
−
4
x
+
5
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
\_\_
__
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
−
6
y = x^2 - 6
y
=
x
2
−
6
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
\_\_
__
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
−
9
2
y = x^2 - \frac{9}{2}
y
=
x
2
−
2
9
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
+
6
x
+
10
y = x^2 + 6x + 10
y
=
x
2
+
6
x
+
10
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
+
4
x
−
4
y = x^2 + 4x - 4
y
=
x
2
+
4
x
−
4
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
+
7
2
y = x^2 + \frac{7}{2}
y
=
x
2
+
2
7
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
+
4
x
+
3
y = x^2 + 4x + 3
y
=
x
2
+
4
x
+
3
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
\_\_
__
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
−
5
2
y = x^2 - \frac{5}{2}
y
=
x
2
−
2
5
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_
_
\_\_
__
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
−
27
5
y = x^2 - \frac{27}{5}
y
=
x
2
−
5
27
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
−
5
x
y = x^2 - 5x
y
=
x
2
−
5
x
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the
y
y
y
-intercept of the parabola
y
=
x
2
−
1
y = x^2 - 1
y
=
x
2
−
1
.
\newline
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
\newline
_____
Get tutor help
Find the equation of the axis of symmetry for the parabola
y
=
x
2
−
3
x
+
4
y = x^2 - 3x + 4
y
=
x
2
−
3
x
+
4
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
_____
Get tutor help
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2
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