# What is the graph of f(x)=-2x^2+7x+4?

Jun 28, 2018

check the explanation below.

#### Explanation:

$y = - 2 {x}^{2} + 7 x + 4$

Take -2 as a common factor from the first two terms and complete the square afterwards

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

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

$y = - 2 {\left(x - \frac{7}{4}\right)}^{2} + 10.125$

it's vertex is $\left(\frac{7}{4} , 10.125\right)$

auxiliary points:

It's intersection with the $x - \text{axis}$

and opened downwards since the coefficient of ${x}^{2}$ is negative

$y = 0 \rightarrow x = - 0.5 \mathmr{and} x = 4$

graph{y=-2x^2+7x+4 [-11.56, 13.76, -1.42, 11.24]}