What's the equation of the parabola that has its vertex at (4,–1) and a y-intercept at (0,7)?
Question 2 options:

A)

y = –1∕2(x + 4)2 – 1

B)

y = 1∕2(x + 4)2 – 1

C)

y = 1∕2(x – 4)2 – 1

D)

y = 1∕2(x – 4)2 + 1

Question

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**HELP ASAP PLZ ;-;** Let f(x)=(x^2+3x-4) and g(x)=(x+4) 1. Find f*g and state the domain 2. Find f/g and state the domain

rosie2276 rosie2276 · Answer 1 · 2020-07-13T09:50:06+02:00

Answer:

C

because it is given that the vertex is (4, - 1) an an equation C it is clearly seen that the vertex is same.

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Yogeshkumari Yogeshkumari · Answer 2 · 2022-05-19T21:00:20+02:00

Equation of parabola with vertex at (4,-1) and y-intercept at (0,7) is equals to y = (1 / 2) (x -4)² - 1.

"Parabola is a U shaped curve, where points on the curve is equidistant from a fixed point."

General equation of parabola with vertex (h, k)

y = a( x- h)² + k

According to the question,

Vertex =( 4, -1)

y-intercept = ( 0,7)

Substitute the value of vertex in equation of parabola , we get

y = a ( x - 4)² + ( -1)

⇒ y = a (x -4)² - 1 _____(1)

Now substitute the value of y-intercept in (1) , we get

7 = a (0 - 4)² - 1

⇒ 16a = 8

⇒ a = 1 / 2

Now again substitute the value of 'a' in (1) , we get

y = ( 1/ 2) (x - 4)² - 1

Hence, we conclude that Option C is correct.

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