Question

How many times does the quadratic function below intersect the x-axis? y= x^2 + 10x +25

A.) 2

B.) 3

C.) 1

D.) 0

Answer 1

The quadratic function is y = x² + 10x + 25.

To find the real zeros of the function, set y equal to zero and solve for x.

 x² + 10x + 25 = 0

x² + 2(5)(x) + 5² = 0

Apply Perfect Square Trinomial : u² + 2uv + v² = (u + v)².

(x + 5)² = 0

x + 5 = 0

x = - 5.

So, the real zero is - 5. Because the function is a second-degree polynomial, the graph of have at most 2 - 1 = 1 turning points.

The option C is correct.