Carolyn Moore

2021-12-06

Write the equation of a quadratic function with roots as -6 and -4, and a vertex at . Write the equation in standard form.
a) $y=-{x}^{2}-10x-24$
b) $y=24{x}^{2}+240x+96$
c) $y={x}^{2}+10x+24$
d) $y=-24{x}^{2}-240x-96$
e) There is no correct answer given.

George Blue

Step 1
Equation of quadratic function with roots at -6 and -4 and vertex
Step 2
If function is $a{x}^{2}+bx+c$
Then $-6-4=\frac{-b}{a}$
$⇒\frac{b}{a}=10$
$\left(-6×-4\right)=24=\frac{c}{a}$
y-intercept
i.e, at
This is satisfied by option (a)
$y=-{x}^{2}-10x-24$

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