a To average the x-intercepts we first need to find them. At an x-intercept, the value of y is 0. Therefore, we will set y equal to 0 and solve the equation using the Quadratic Formula.
All parabolas are symmetric about their vertex. What this means is if two points have the same y-coordinate, such as the x-intercepts, they are equidistant from the parabola's line of symmetry. Therefore, we can find the line of symmetry by averaging the x-intercepts.
The line of symmetry is x_s=4 which is the x-value of the vertex. We can find the corresponding y-value by substituting 4 for x in the function and evaluating the right-hand side.
Graphing Form:& y=a(x-h)^2+k
Vertex:& (h,k)Completing the square requires us to add the square of half the coefficient of x to both sides of the equation.
To identify the vertex, we have to rewrite the function so that it matches the graphing form exactly.
Function:& y=(x-4)^2+(-6)
Vertex:& (4,-6)
The vertex of the quadratic function is (4,-6).
c Let's use the method of averaging the x-intercepts. To find the x-intercepts, we will solve the equation when y=0. To do that, we factor out x and then use the Zero Product Property.
