Question

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

Answer 1

A. 1

Explanation:

To find the x-intercept, substitute 0 for y and solve for x.

x-intercept(s): (-5,0)

Considering (-5,0) is the only intersection on the x-axis, 1 is your answer.

If you want a visual of this, I recommend you use the Desmos graphing calculator to input your equation. It will show you what the curved line looks like.

Answer 2

To find how many times the quadratic function intersects the x-axis, set y = 0

y = x^2+10x+25
0 = x^2+10x+25
Factor the right hand side
0 = (x+5)(x+5)
x + 5 = 0
x = - 5

Therefore, the quadratic equation intersects the x-axis at one point (x = -5)