The x-intercept(s) of the parabola is x = -4 and the vertex of the parabola is (-4, 0)
Parabola equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
The x-intercepts
The parabola is given as:
y=x^2+8x+16
Expand the equation
y = x^2 + 4x + 4x +16
Factorize the equation
y = (x + 4)^2
Set the factor to 0
(x + 4)^2 = 0
Take the square root of both sides
x + 4 = 0
Solve for x
x = -4
Hence, the x-intercept(s) of the parabola is x = -4
The vertex
The parabola is given as:
y=x^2+8x+16
Differentiate
y' = 2x + 8
Set the equation to 0
2x + 8 = 0
Divide through by 2
x + 4 = 0
Solve for x
x = -4
Substitute x = -4 in y=x^2+8x+16
y = (-4)^2 + 8(-4) + 16
Evaluate
y = 0
Hence, the vertex is (-4, 0)
Read more about parabolas at:
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