Y=x^2+bx+c;(-2,3) For the function, the vertex of the function's graph is given. Find the unknown coefficients.

Question

asked Mar 27, 2021 130k views

1 Answer

Sarcastron · Answer 1 · 2021-03-31T13:42:54+0000

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Step-by-step explanation:

Comparing y = x^2+bx+c to y = ax^2+bx+c, we see that a = 1.

The vertex given is (-2,3). In general, the vertex is (h,k). So h = -2 and k = 3.

Plug those three values into the vertex form below

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

y = 1(x-(-2))^2 + 3

y = (x+2)^2 + 3

Then expand everything out and simplify

y = x^2+4x+4 + 3

y = x^2+4x+7

We see that b = 4 and c = 7.