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klemol [59]
3 years ago
6

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

Mathematics
1 answer:
natka813 [3]3 years ago
4 0

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 <em>x</em>-intercepts of our quadratic. Intercept or factored form is given by:

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

Where <em>p</em> and <em>q</em> are the <em>x</em>-intercepts, and <em>a</em> is the leading coefficient.

So, we will substitute -4 and 2 for <em>p</em> and <em>q: </em>

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

Simplify:

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

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

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

Solve for <em>a: </em>

-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)

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