Answer: 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
y = -0.07(x + 10)(x - 10)
NOTE: You can convert this into the standard form by multiplying
y = -0.07(x² - 100)
y = -0.07x² + 7
