Question

What is the quadratic function that is created with roots -10 and -4 and a vertex at (-7, -9)?

Answer 1

Help

Answer 2

If the roots of the quadratic are \(-10\) and \(-4\), then

\(x + 10 = 0\)
\(x + 4 = 0\)

And \((x + 10)(x - 4) = 0\)

Multiply the left side of the quadratic equation to get the form \(ax^2 + bx + c = 0\)

Then use \(x = -\dfrac{b}{2a}\) to find the \(x\) coordinate of the vertex.

Answer 3

Actually the quadratic equation should be \((x+10)(x + 4) = 0\)

Answer 4

so it would be x^2+14x+40

Answer 5

Yes, now verify that the vertex is (-7,-9)

Answer 6

wait so x^2+14x+40 is my final answer

Answer 7

?

Answer 8

Only after you have verified the vertex.

Answer 9

how do i do that

Answer 10

Find the x coordinate using the formula I gave you above.

Answer 11

x=-7

Answer 12

thts wat i got

Answer 13

Good now, plug that into the quadratic expression, then simplify

Answer 14

i got -9

Answer 15

Very good

Answer 16

so my final answer is : the quadratic function that is created with roots -10 and -4 and a vertex at (-7, -9) is x^2+14x+40

Answer 17

Yes, and of course include all the steps you did to arrive at that conclusion.

Answer 18

ok thank u so much for ur help

Answer 19

you're welcome