The problem asks to find the y-intercept and x-intercepts of the quadratic equation $y = x^2 - 2x - 15$.

AlgebraQuadratic EquationsInterceptsFactorizationCoordinate Geometry
2025/6/4

1. Problem Description

The problem asks to find the y-intercept and x-intercepts of the quadratic equation y=x22x15y = x^2 - 2x - 15.

2. Solution Steps

To find the y-intercept, we set x=0x = 0 and solve for yy.
y=(0)22(0)15y = (0)^2 - 2(0) - 15
y=15y = -15
So the y-intercept is at the point (0,15)(0, -15).
To find the x-intercepts, we set y=0y = 0 and solve for xx.
0=x22x150 = x^2 - 2x - 15
We can factor the quadratic expression:
0=(x5)(x+3)0 = (x - 5)(x + 3)
Setting each factor equal to zero:
x5=0x - 5 = 0 or x+3=0x + 3 = 0
x=5x = 5 or x=3x = -3
So the x-intercepts are at the points (5,0)(5, 0) and (3,0)(-3, 0).

3. Final Answer

The y-intercept is (0,15)(0, -15).
The x-intercepts are (5,0)(5, 0) and (3,0)(-3, 0).