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

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Answer 1 · 2018-06-28T14:18:26

check the explanation below.

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

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

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

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

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

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

auxiliary points:

It's intersection with the $x - axis$ $x-"axis"$

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

$y = 0 \to x = - 0.5 or x = 4$ $y=0rarr x=-0.5 or x=4$

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

What is the graph of f(x)=−2x2+7x+4f(x)=-2x^2+7x+4?