Question

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

Answer 1

Answer:

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

Step-by-step explanation:

The given quadratic function is

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

Where $a=8$, $b=2$ and $c=-5$.

Now, let's find the vertex, which coordinates are $V(h,k)$, and $h=-\frac{b}{2a}$

Replacing each value, we have

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

Then, $k=f(h)$, so

$f(-\frac{1}{8} )=8(-\frac{1}{8} )^{2} +2(-\frac{1}{8} )-5=\frac{1}{8}-\frac{1}{4} -5=\frac{1-2-40}{8}\\ k=-\frac{41}{8}$

So, the vertex is

$V(-\frac{1}{8},-\frac{41}{8})$ and $a=8$

Therefore, the vertex form is

$y=a(x-h)^{2}+k\\ y=8(x+\frac{1}{8} )^{2} -\frac{41}{8}$

Answer 2

Hello : 
f(x) = 8x² + 2x - 5
f(x) = 8(x²+1/4 x)-5
f(x) = 8(x²+2(1/8)x +(1/8)² -(1/8)² ) -5
f(x) = 8((x+1/8)²-1/8-5
f(x) = 8(x+1/8)²-41/5....(vertex form)