Tyler's dog jumps over fences like a pro. When he stands 10 feet away from the fence, he can clear a 7 foot tall fence, and land 10 feet from the fence on the other side. If his jump matches a parabolic graph, what is the equation of his jump?

Intercept form:  y = -0.07(x + 10)(x - 10)  

              Standard form:  y = -0.07x² + 7

Step-by-step explanation:

Step 1: Draw a picture to understand what the parabola looks like.

Let the y-axis represent the fence --> coordinate = (0, 7)

 Let the x-intercepts represent the points where the dog starts to jump

 and also where the dog lands --> coordinates = (-10, 0) & (10, 0)

 (see attached graph).

Step 2: Use the intercept form of a parabola -->  y = a(x - p)(x - q)

            where p & q are the x-intercepts and a is the vertical stretch

            Given: p = -10    and q = 10

            y = a(x + 10)(x - 10)

Step 3: Input (x, y) of a 3rd coordinate into the equation to find the a-value

            3rd coordinate (not the x-intercepts) = (0, 7) → x=0, y=7

             7 = a(0 + 10)(0 - 10)

             7 = a(10)(-10)

             7 = -100a

             -0.07 = a         divided both sides by -100

Step 4: Input the a-value and x-intercepts into the intercept formula

NOTE: You can convert this into the standard form by multiplying

            y = -0.07(x² - 100)

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8

the answer is 13/48

step-by-step explanation: