Question

Write the equation of the quadratic function with roots -1 and -7 and a vertex at (-4, 7)

Answer 1

Roots at -1 and -7 so will have the form:
\[y=a(x+1)(x+7)\]
Substitute x=-4, y=7 to find a. Can you have a go?

Answer 2

\[y=a(x+1)(x+7)\]
So that when you set y=0 (i.e. on the x-axis), x satisfies
\[0=a(x+1)(x+7)\] when it is equal to -1 or -7

Answer 3

7=a(-4+1)(-4+7)

Answer 4

Yep, so:
\[7=a\times(-3)\times(3)\]
\[7=-9a\]
\[a=\frac{-7}{9}\]
Now do you see what the equation will be with this value of a?

Answer 5

y=7(x+1)(x=7) ?

Answer 6

@Traxter

Answer 7

Not quite, if you substitue a=-7/9 into the equation I wrote before:
\[y=a(x+1)(x+7)\]
Then you will have:
\[y=\frac{-7}{9}(x+1)(x+7)\]
Agree?

Answer 8

yes!!

Answer 9

thank youuuuuuuu

Answer 10

and @henpen

Answer 11

Welcome :)