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symmetry to sketch a graph
qquad of the function
y=36x^(2)-100.
Label the intersection point for the axis of symmetry and the roots.

Add a new expression using the + in the upper left, then choose expression.
Type in a point you want to label using an ordered pair.
Example:
(1,0)
Choose the Label checkbox.

Once complete, choose the line that is the axis of symmetry.

symmetry to sketch a graph $\qquad$ of the function $y=36 x^{2}-100$ . $\newline$ Label the intersection point for the axis of symmetry and the roots. $\newline$ - Add a new expression using the + in the upper left, then choose expression. $\newline$ - Type in a point you want to label using an ordered pair. $\newline$ - Example: $(1,0)$ $\newline$ - Choose the Label checkbox. $\newline$ Once complete, choose the line that is the axis of symmetry.

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Conjugate root theorems

Full solution

Q. symmetry to sketch a graph

\qquad

of the function

y=36 x^{2}-100

.

\newline

Label the intersection point for the axis of symmetry and the roots.

\newline

- Add a new expression using the + in the upper left, then choose expression.

\newline

- Type in a point you want to label using an ordered pair.

\newline

- Example:

(1,0)

\newline

- Choose the Label checkbox.

\newline

Once complete, choose the line that is the axis of symmetry.

Find Vertex: Find the vertex of the parabola. The vertex form of a parabola is $y=a(x-h)^2+k$ , where $(h,k)$ is the vertex. For $y=36x^2-100$ , the vertex is at $(0,-100)$ because there is no $(x-h)$ part, so $h=0$ , and $k=-100$ .
Determine Axis of Symmetry: Determine the axis of symmetry. The axis of symmetry is $x=h$ . Since $h=0$ , the axis of symmetry is the y-axis, or $x=0$ .
Find Roots: Find the roots by setting $y=0$ and solving for $x$ . $0=36x^2-100$ . Add $100$ to both sides: $36x^2=100$ . Divide by $36$ : $x^2=\frac{100}{36}$ . Take the square root of both sides: $x=\pm\sqrt{\frac{100}{36}}, x=\pm\sqrt{\frac{25}{9}}, x=\pm\frac{5}{3}.$
Label Intersection Point: Label the intersection point for the axis of symmetry, which is the vertex $(0,-100)$ .
Label Roots: Label the roots, which are the x-intercepts $\frac{5}{3},0$ and $\frac{-5}{3},0$ .
Draw Parabola: Draw the parabola opening upwards with the vertex at $(0,-100)$ and passing through the roots at $(\frac{5}{3},0)$ and $(-\frac{5}{3},0)$ . The axis of symmetry is the line $x=0$ .

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