Question

What is f(x) = 2x2 + 28x – 5 written in vertex form? f(x) = 2(x + 7)2 – 19 f(x) = 2(x + 7)2 – 103 f(x) = 2(x + 14)2 – 14 f(x) = 2(x + 14)2 – 98

Answer 1

Answer: B. f(x) = 2(x + 7)² - 103

Step-by-step explanation:

$y=2x^2+28x-5\\\\\\y+5=2x^2+28x\\\\\\y+5=2(x^2+14x+\underline{\quad}\ )\\.\qquad \qquad \qquad \ \ \downarrow\\.\qquad \qquad \qquad \bigg(\dfrac{14}{2}\bigg)^2=7^2 \\\\\\y + 5 + 2(7)^2=2(x^2+14x+\underline{7^2} )\\\\\\y + 5 + 98 = 2(x + 7)^2\\\\\\y+103=2(x+7)^2\\\\\\y=2(x+7)^2-103$

Answer 2

Answer:

f(x)=2(x+7)^2-103

Step-by-step explanation:

$f(x)=2x^{2} +28x-5\\=2(x^2+14x)-5\\=2(x^2+2(7)x+7^2-7^2)-5\\=2(x+7)^2-2(49)-5\\=2(x+7)^2-103$