Question

y = 3x^2 + 12x - 7 Vertex form

Answer 1

To express the equation y = 3x^2 + 12x - 7 in vertex form, we first need to complete the square.

y = 3(x^2 + 4x) - 7

Next, we need to find the value that completes the square inside the parenthesis. To do this, we take half of the coefficient of x (4) and square it:

(4/2)^2 = 2^2 = 4

Now, we add and subtract this value inside the parenthesis:

y = 3(x^2 + 4x + 4 - 4) - 7
y = 3((x + 2)^2 - 4) - 7
y = 3(x + 2)^2 - 12 - 7
y = 3(x + 2)^2 - 19

Therefore, the vertex form of the equation y = 3x^2 + 12x - 7 is y = 3(x + 2)^2 - 19.