Question

what is the vertex form of y=2x^2-8x+1

Answer 1

Answer:

$2(x-2)^2-7$

Step-by-step explanation:

$y=2x^2-8x+1$

When comparing to standard form of a parabola: $ax^2+bx+c$

• $a=2$
• $b=-8$
• $c=1$

Vertex form of a parabola is: $a(x-h)^2+k$, which is what we are trying to convert this quadratic equation into.

To do so, we can start by finding "h" in the original vertex form of a parabola. This can be found by using: $\frac{-b}{2a}$.

Substitute in -8 for b and 2 for a.

$\frac{-(-8)}{2(2)}$

Simplify this fraction.

$\frac{8}{4} \rightarrow2$

$\boxed{h=2}$

The "h" value is 2. Now we can find the "k" value by substituting in 2 for x into the given quadratic equation.

$y=2(2)^2-8(2)+1$

Simplify.

$y=-7$

$\boxed{k=-7}$

We have the values of h and k for the original vertex form, so now we can plug these into the original vertex form. We already know a from the beginning (it is 2).

$a(x-h)^2+k\\ \\ 2(x-2)^2-7$