# What is the vertex form of  f(x) = -2x^2+7x-12 ?

##### 1 Answer
Mar 25, 2017

Given the standard form of a parabola:

$f \left(x\right) = a {x}^{2} + b x + c$

The vertex form is:

$f \left(x\right) = a {\left(x - h\right)}^{2} + k$

Please see the explanation for the conversion process.

#### Explanation:

Given the specific equation in standard form:

$f \left(x\right) = - 2 {x}^{2} + 7 x - 12$

Here is the graph:

graph{-2x^2+7x-12 [-26.5, 38.46, -33.24, 0.58]}

Comparing with the standard form:

$a = - 2 , b = 7 , \mathmr{and} c = - 12$

You obtain the value of "a" by observation:

$a = - 2$

To obtain the value of h, use the equation:

$h = - \frac{b}{2 a}$

h = -7/(2(-2)

$h = \frac{7}{4}$

To obtain the value of k, evaluate the function at $x = h$:

$k = - 2 {\left(\frac{7}{4}\right)}^{2} + 7 \left(\frac{7}{4}\right) - 12$

$k = - \frac{94}{16}$

Substituting these values into the vertex form:

$f \left(x\right) = - 2 {\left(x - \frac{7}{4}\right)}^{2} - \frac{94}{16}$