Mathematics: Y=(x+5) (x+4) in vertex form of parabola

Y=(x+5) (x+4) in vertex form of parabola

Ответ:

frisha

13.01.2022

Mathematics

Step-by-step explanation:

The vertex form of an equation of a parabola y = ax² + bx + c:

y=a(x-h)^2+k

(h, k) - verex

$h=\dfrac{-b}{2a},\ k=f(h)$

We have:

y=(x+5)(x+4) use FOIL (a + b)(c + d) = ac + ad + bc + bd

y=(x)(x)+(x)(4)+(5)(x)+(5)(4)=x^2+4x+5x+20=x^2+9x+20

a = 1, b = 9, c = 20

$h=\dfrac{-9}{2(1)}=\dfrac{-9}{2}=-\dfrac{9}{2}$

For k, put the value of h to the equation y = (x + 5)(x + 4):

$k=\left(-\dfrac{9}{2}+5\right)\left(-\dfrac{9}{2}+4\right)\\\\k=\left(-\dfrac{9}{2}+\dfrac{10}{2}\right)\left(-\dfrac{9}{2}+\dfrac{8}{2}\right)\\\\k=\left(\dfrac{1}{2}\right)\left(-\dfrac{1}{2}\right)=-\dfrac{1}{4}$

Finally:

$y=1\bigg(x-\left(-\dfrac{9}{2}\right)\bigg)^2-\dfrac{1}{4}\\\\y=\left(x+\dfrac{9}{2}\right)^2-\dfrac{1}{4}$

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Ответ:

Maddy8368

21.01.2022

Mathematics

First # is 169

Second # is 171

There are no consecutive even numbers that add up to 340

Step-by-step explanation:

x + x + 2 = 340

2x + 2 = 340

2x = 338

x = 169

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Y=(x+5) (x+4) in vertex form of parabola

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