Carolyn Moore

2021-12-06

Write the equation of a quadratic function with roots as -6 and -4, and a vertex at $(0,\text{}-24)$ . 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.

a)

b)

c)

d)

e) There is no correct answer given.

George Blue

Beginner2021-12-07Added 18 answers

Step 1

Equation of quadratic function with roots at -6 and -4 and vertex$(0,\text{}-24)$

Step 2

If function is$a{x}^{2}+bx+c$

Then$-6-4=\frac{-b}{a}$

$\Rightarrow \frac{b}{a}=10$

$(-6\times -4)=24=\frac{c}{a}$

y-intercept$\Rightarrow (0,\text{}-24)$

i.e, at$x=0,\text{}y=-24$

This is satisfied by option (a)

$y=-{x}^{2}-10x-24$

Equation of quadratic function with roots at -6 and -4 and vertex

Step 2

If function is

Then

y-intercept

i.e, at

This is satisfied by option (a)