Question

Use the​ x-intercepts of the parabola and the given point to write a quadratic function in factored form.
-8
2
-17
9
x
y
left parenthesis 0 comma negative 7 right parenthesis(0,−7)



x y graph
Question content area bottom
Part 1
The quadratic function in factored form is ​f(x)equals=enter your response here.

Answer 1

To write a quadratic function in factored form using x-intercepts and a given point, we start with the general form of a quadratic function given in factored form:

\[
f(x) = a(x - r_1)(x - r_2)
\]

where \( r_1 \) and \( r_2 \) are the x-intercepts of the parabola.

From your input, it seems the x-intercepts are \(-8\) and \(2\). Therefore, we can write:

\[
f(x) = a(x + 8)(x - 2)
\]

Next, we need to find the value of \(a\). To do this, we will use the given point \((0, -7)\). We can substitute \(x = 0\) and \(f(x) = -7\) into the function:

\[
-7 = a(0 + 8)(0 - 2)
\]

This simplifies to:

\[
-7 = a(8)(-2)
\]
\[
-7 = -16a
\]

Now, solving for \(a\):

\[
a = \frac{-7}{-16} = \frac{7}{16}
\]

Now substitute \(a\) back into the function:

\[
f(x) = \frac{7}{16}(x + 8)(x - 2)
\]

Thus, the quadratic function in factored form is:

\[
f(x) = \frac{7}{16}(x + 8)(x - 2)
\]