Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write the equation in vertex form for the parabola with vertex (0,−2)(0,-2) and directrix y=6y = 6.\newlineSimplify any fractions.\newline______

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Write equations of parabolas in vertex form using propertiesright chevron icon

Full solution

Q. Write the equation in vertex form for the parabola with vertex (0,−2)(0,-2) and directrix y=6y = 6.\newlineSimplify any fractions.\newline______
  1. Identify Parabola Orientation: Since the directrix is y=6y = 6, the parabola is vertical and opens downward because the vertex (0,−2)(0,-2) is below the directrix.
  2. Vertex Form of Parabola: The vertex form of a vertical parabola is y=a(x−h)2+ky = a(x-h)^2 + k, where (h,k)(h,k) is the vertex.
  3. Calculate Distance to Directrix: The distance between the vertex and the directrix is ∣6−(−2)∣=8|6 - (-2)| = 8.
  4. Determine Focus Value: Since the parabola opens downward, aa is negative. The focus is the same distance from the vertex as the directrix, so a=−14⋅8=−132a = -\frac{1}{4\cdot8} = -\frac{1}{32}.
  5. Substitute Values into Equation: Substitute a=−132a = -\frac{1}{32} and the vertex (h,k)=(0,−2)(h,k) = (0,-2) into the vertex form equation: y=−132(x−0)2−2y = -\frac{1}{32}(x-0)^2 - 2.
  6. Simplify Equation: Simplify the equation: y=−132x2−2y = -\frac{1}{32} x^2 - 2.

More problems from Write equations of parabolas in vertex form using properties

Question
What is the focus of the parabola y=−x2y = -x^2?\newlineSimplify any fractions.\newline(_____ , _____)\newline
Get tutor helpright-arrow

Posted 1 month ago

Question
The equation of a parabola is y=x2−10x+25y = x^2 - 10x + 25. Write the equation in vertex form.\newlineWrite any numbers as integers or simplified proper or improper fractions.\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
In which direction does the parabola x+y2=−7x + y^2 = -7 open?\newlineChoices:\newline(A) up\text{up}\newline(B) down\text{down}\newline(C) right\text{right}\newline(D) left\text{left}
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the vertex of the parabola y=−4(x−2)2+2y = -4(x - 2)^2 + 2??\newline(_,_)(\_,\_)
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the axis of symmetry of the parabola x=12(y+3)2+5x = \frac{1}{2}(y + 3)^2 + 5?
Get tutor helpright-arrow

Posted 2 months ago

Question
In which direction does the parabola x−2y2=−5x - 2y^2 = -5 open?\newlineChoices:\newline[A]up\text{[A]up}\newline[B]down\text{[B]down}\newline[C]right\text{[C]right}\newline[D]left\text{[D]left}
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the vertex of the parabola y−8x2=4y - 8x^2 = 4? \newline(_,_)(\_,\_)
Get tutor helpright-arrow

Posted 1 month ago

Question
The equation of a circle is x2+(y+4)2=1 x^{2}+(y+4)^{2}=1 . What are the center and radius of the circle?\newlineChoose 11 answer:\newline(A) The center is (−4,0) (-4,0) and the radius is 11 .\newline(B) The center is (4,0) (4,0) and the radius is 11 .\newline(C) The center is (0,4) (0,4) and the radius is 11 .\newline(D) The center is (0,−4) (0,-4) and the radius is 11 .
Get tutor helpright-arrow

Posted 4 months ago

Question
y=(x−3)(x+9) y=(x-3)(x+9) \newlineThe given equation is graphed in the xy x y -plane. Which of the following are x x -intercepts of the graph?\newlineChoose 11 answer:\newline(A) −3-3 and −9-9\newline(B) −3-3 and 99\newline(C) 33 and −9-9\newline(D) 33 and 99
Get tutor helpright-arrow

Posted 4 months ago

Question
If y=2x2−5x+7 y=2 x^{2}-5 x+7 is graphed in the xy x y -plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?\newlineChoose 11 answer:\newline(A) x x -intercept(s)\newline(B) y y -intercept\newline(C) x x -coordinate of the vertex\newline(D) y y -coordinate of the vertex
Get tutor helpright-arrow

Posted 4 months ago

View all (39)