Question

use the x-intercepts of the parabola and the given point to write a quadratic function in factored form.

the quadratic function in factored form is f(x) =

Explanation:

Identify the x-intercepts from the graph

The graph shows a parabola crossing the x-axis.
Looking closely at the grid:

• The left x-intercept is at \(x = -6\).
• The right x-intercept is at \(x = 1\).

Thus, the roots are \(p = -6\) and \(q = 1\).

Set up the factored form equation

Using the Graphing Quadratic Functions concept, the factored form of a quadratic function is:

$$f(x) = a(x - p)(x - q)$$

Substituting the identified intercepts:

$$f(x) = a(x - (-6))(x - 1) = a(x + 6)(x - 1)$$

Use the given point to solve for a

The graph explicitly labels a point on the parabola: \((0, -6)\).
Substitute \(x = 0\) and \(f(x) = -6\) into the equation:

$$-6 = a(0 + 6)(0 - 1)$$

$$-6 = a(6)(-1)$$

$$-6 = -6a$$

$$a = 1$$

Write the final factored form

Substitute \(a = 1\) back into the factored form equation:

$$f(x) = 1(x + 6)(x - 1)$$

Simplifying, we get:

$$f(x) = (x + 6)(x - 1)$$

Answer:

Use the x-intercepts of the parabola and the given point to write a quadratic function in factored form.

The quadratic function in factored form is f(x) = <blank>\((x + 6)(x - 1)\)</blank>.