Find the x and y Intercepts y=x^2+8x+12

Problem

y=x2+8*x+12

Solution

1. Find the y-intercept by setting x=0 in the equation.

y=(0)2+8*(0)+12

y=12

2. Find the x-intercepts by setting y=0 and solving the resulting quadratic equation.

0=x2+8*x+12

3. Factor the quadratic expression by finding two numbers that multiply to 12 and add to 8

0=(x+6)*(x+2)

4. Apply the Zero Product Property by setting each factor equal to zero.

x+6=0⇒x=−6

x+2=0⇒x=−2

Final Answer

x-intercepts: *(−6,0),(−2,0); y-intercept: *(0,12)

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