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

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Answer 1 · 2017-03-25T16:43:27

Given the standard form of a parabola:

$f(x)=ax^2+bx+c$

The vertex form is:

$f(x)=a(x-h)^2+k$

Please see the explanation for the conversion process.

Given the specific equation in standard form:

$f(x) = -2x^2+7x-12$

Here is the graph:

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

Comparing with the standard form:

$a = -2, b = 7, and c = -12$

You obtain the value of "a" by observation:

$a = -2$

To obtain the value of h, use the equation:

$h = -b/(2a)$

$h = -7/(2(-2)$

$h = 7/4$

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

$k = -2(7/4)^2+7(7/4)-12$

$k = -94/16$

Substituting these values into the vertex form:

$f(x) = -2(x-7/4)^2-94/16$

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