Question 296136: Find any x-intercepts and the y-intercepts. If no x-intercepts exist, state this.
g(x)=x^2-6x+9
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! g(x)=x^(2)-6x+9
To find the x-intercept, substitute in 0 for y and solve for x.
(0)=x^(2)-6x+9
Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
x^(2)-6x+9=(0)
Any expression with zero in the numerator is zero.
x^(2)-6x+9=0
Factor the trinomial x^(2)-6x+9.
(x-3)(x-3)=0
Set each of the factors of the left-hand side of the equation equal to 0.
x-3=0
Since -3 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3 to both sides.
x=3
To find the y-intercept, substitute in 0 for x and solve for y.
y=(0)^(2)-6(0)+9
Any expression with zero in the numerator is zero.
y=0-6(0)+9
Multiply -6 by each term inside the parentheses.
y=0+0+9
Solve the equation.
y=9
These are the x and y intercepts of the equation y=x^(2)-6x+9.
x=3, y=9
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