Find the x and y Intercepts y=x^2-10x+21

Problem

y=x2−10*x+21

Solution

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

y=0−10*(0)+21

y=21

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

0=x2−10*x+21

3. Factor the quadratic expression by finding two numbers that multiply to 21 and add to −10

0=(x−3)*(x−7)

4. Solve for x by setting each factor equal to zero using the zero product property.

x−3=0⇒x=3

x−7=0⇒x=7

Final Answer

x-intercepts: *(3,0),(7,0); y-intercept: *(0,21)

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