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
