List the x-intercepts for this parabola and the x-coordinate of the vertex:
What math procedure could you use to calculate the x-coordinate of the vertex from only the x-intercepts? Seeing that parabolas are symmetrical, in order for one to calculate the x-coordinate of the vertex from the x-intercepts, one can simply add the x-values for the intercepts and divide them by 2. By doing that, one will obtain the x-coordinate of the vertex, which should be at the midpoint between both intercepts. Demonstrate how you find the y-coordinate of the vertex in this case from the x-coordinate (3) and the quadratic equation given [ y = (7-x)(1+x) ]. In order to find the y-coordinate all one must do is plug in the value for x in the quadratic equation for the parabola. In this case: y = (7-3)(1+3) => y = 16
y = (7-x)(1+x) => y = 7+7x-x-x2 => y = -x2+6x+7
Give the formula for the axis of symmetry, show how the axis of symmetry can be found from the standard form quadratic equation, and that it is equal to the x-coordinate of the vertex found earlier.
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