Write the quadratic function in vertex form. y = x2 + 4x + 7

Complete the square on the right side of the equation.

Use the form ax^2 + bx + cax^2 + bx + c, to find the values of aa , bb, and cc.

a=1, b=4, c=7

Consider the vertex form of a parabola.

a(x + d)^2  + e

Find the value of d using the formula d = b / 2a

Multiply 2 by 1 to get 2 ⋅ 1.

d = 4 / (2 * 1)

d = 2

Find the value of e using the formula e =c −b^2 / 4a

Multiply 4 by 1 to get 4 ⋅ 1

E = 7 – ((4)^2 / (4 ⋅ 1))

Reduce the expression by cancelling the common factors.

E = 7 – 1 ⋅ 4

Subtract 44 from 77 to get 33.

e = 3

Substitute the values of a, d, and e into the vertex form a(x + d)^2 + e.

(x +  2)^2 + 3

Therefore, the vertex form of the quadratic equation is:

y = (x + 2)^2 + 3

b

step-by-step explanation: