Determine the quadratic function of a parabola with x-intercepts x = 7 andx = -2 and y-intercept y = 5

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embizze | High School Teacher | (Level 2) Educator Emeritus

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We are given the two x-intercepts as x=-2,x=7 and the y-intercept y=5.

The intercept form form a parabola is y=a(x-p)(x-q) where p,q are the x-intercepts and a determines how wide the parabola opens. (Also, if a<0 the parabola opens down.)

Substituting -2 for p and 7 for q we get:


Now the y-intercept is the point where x=0; substituting for x we solve for a:

5=a(0+2)(0-7) ==> 5=-14a ==> `a=-5/14`


The equation is `y=-5/14(x+2)(x-7)` .

In standard form: `y=-5/14x^2+25/14x+5`


The graph:

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