hush asked in Science & MathematicsMathematics · 1 month ago

# Function f(x) = a(x+1)(x-3) has a vertex at (1, -16). Find a.?

Function f(x) = a(x+1)(x-3) has a vertex at (1, -16). Find a.

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• 1 month ago

f(x)=a(x+1)(x-3)

=>

-16=a(1+1)(1-3)

=>

-16=-4a

=>

a=4

• 1 month ago

f(x) = a(x + 1)(x - 3)

The vertex is (1, -16), so that means f(1) = -16.

Just plug in those values and you have:

-16 = a(1 + 1)(1 - 3)

It's simple algebra from there. You can do it!

• 1 month ago

y = a(x+1)(x-3)

y = a(x² – 2x – 3)

y(1/a) = x² – 2x – 3

y(1/a) + 4 = x² – 2x + 1

y(1/a) + 4 = (x – 1)²

the x cord of the vertex is indeed at 1

y cord;

4p(y–k) = y(1/a) + 4

k = –16

4p(y+16) = y(1/a) + 4

4py + 64p = y(1/a) + 4

if 64p = 4, p = 4/64 = 1/16

4p = 1/a

4/16 = 1/4 = 1/a

a = 4

y = a(x² – 2x – 3)

y = 4(x² – 2x – 3)

or

y = 4(x + 1)(x – 3)

Parabola vertical

4p(y–k) = (x–h)²

p is distance vertex to focus, if positive opens up

p is also distance vertex to directorix

vertex at (h, k)

• rotchm
Lv 7
1 month ago

You are told that -16 = a(1+1)(1-3). Convince yourself of this.

Now, can you solve for "a" ? Done!

Hopefully no one will spoil you the answer thereby depriving you from your personal enhancement; that would be very inconsiderate of them.

• 1 month ago

You are given the function and a point, which includes x and y.  Substitute and solve for the unknown:

f(x) = a(x + 1)(x - 3)

x = 1

f(x) = -16

-16 = a(1 + 1)(1 - 3)

-16 = a(2)(-2)

-16 = -4a

4 = a