Question

Write the quadratic function in vertex form: f(x) = 8x2 + 2x - 5

Answer 1

The given function is

f(x) = $8x^{2}+2x-5$

Comparing with

$ax^{2}+bx+c$

We get

a = 8, b = 2 & c = -5

Now if (h,k) is the vertex

then h =$-\frac{b}{2a}=-\frac{2}{2(8)}=-\frac{1}{8}$

Substituting the value of h in place of x in the function we get

k=$8(-\frac{1}{8})^2+2(-\frac{1}{8})-5 = -\frac{41}{8}$

Now the vertex form of a quadratic equation is

f(x)= a(x-h)² + k

Substituting the values of a, h & k we get

f(x) = 8$8(x-(-\frac{1}{8}))^2+(-\frac{41}{8})$

The vertex form of f(x) = 8x² +2x-5 is

f(x) = $8(x+\frac{1}{8})^2-\frac{41}{8}$

Answer

Answer 2

Y=8x²+2x-5
y+5=8(x²+x/4)
y+41/8=8(x²+x/4+1/64)
y+41/8=8(x+1/8)²
f(x)=8(x+1/8)²-41/8