Question

Write a quadratic function in the given form whose graph satisfies the given condition.

Answer 1

Answer:

$\displaystyle y=-\frac{1}{2}(x+4)(x-2)$

Step-by-step explanation:

We want to find a quadratic that passes through the points:

$(-4, 0), \, (2, 0), \text{ and } (6, -20)$

In intercept form.

First, note that the first two given points are the x-intercepts of our quadratic. Intercept or factored form is given by:

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

Where p and q are the x-intercepts, and a is the leading coefficient.

So, we will substitute -4 and 2 for p and q:

$y=a(x-(-4))(x-(2))$

Simplify:

$y=a(x+4)(x-2)$

Next, the third point (6, -20) tells us that y = -20 when x = 6. So:

$(-20)=a(6+4)(6-2)$

Solve for a:

$-20=10(4)a\Rightarrow 40a=-20$

Thus:

$\displaystyle a=\frac{-20}{40}=-\frac{1}{2}$

Hence, our equation in intercept from is:

$\displaystyle y=-\frac{1}{2}(x+4)(x-2)$