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In the
xy-plane, the graph of a quadratic function has
x-intercepts at
(-3,0) and
(7,0). If the parabola has an axis of symmetry of
x=h, then what is the value of
h ?

In the $x y$ -plane, the graph of a quadratic function has $x$ -intercepts at $(-3,0)$ and $(7,0)$ . If the parabola has an axis of symmetry of $x=h$ , then what is the value of $h$ ?

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Write a quadratic function from its x-intercepts and another point

Full solution

Q. In the

x y

-plane, the graph of a quadratic function has

x

-intercepts at

(-3,0)

and

(7,0)

. If the parabola has an axis of symmetry of

x=h

, then what is the value of

h

?

Parabola x-intercepts: The x-intercepts of the parabola are the points where the parabola crosses the x-axis. These are given as $(-3,0)$ and $(7,0)$ . The axis of symmetry of a parabola is exactly halfway between the x-intercepts.
Find axis of symmetry: To find the axis of symmetry, we can average the $x$ -values of the $x$ -intercepts. The formula for the axis of symmetry is $h = \frac{x_1 + x_2}{2}$ , where $x_1$ and $x_2$ are the $x$ -coordinates of the $x$ -intercepts.
Substitute x-intercepts: Substitute the given x-intercepts into the formula: $h = \frac{{-3 + 7}}{2}$ .
Calculate h: Calculate the value of h: $h = \frac{4}{2}$ .
Simplify result: Simplify the result to find the axis of symmetry: $h = 2$ .

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