given the table values, compete the table for the quadratic equation 3x^2 - 6x + 9 to find the values of the high or low point of the parabola
To determine the values of the high or low point of the quadratic equation 3x^2 - 6x + 9, we can complete the square.
Starting with the equation in standard form:
y = 3x^2 - 6x + 9
Step 1: Divide the equation by the coefficient of x^2 to get a coefficient of 1 for x^2.
Dividing by 3, we get:
y = (3/3)x^2 - (6/3)x + 9/3
Simplifying, we have:
y = x^2 - 2x + 3
Step 2: Move the constant term (in this case, 3) to the other side of the equation.
y - 3 = x^2 - 2x
Step 3: To complete the square, take half of the coefficient of x, square it, and add it to both sides of the equation.
y - 3 + 1 = x^2 - 2x + 1
y - 2 = (x - 1)^2
Step 4: Rearrange the equation to vertex form.
y = (x - 1)^2 + 2
Comparing this equation, the vertex is at the point (1, 2). So the values of the high or low point of the parabola are (1, 2).