Question

How do you write the quadratic function in intercept form given x intercepts -10,-8 and point (1,-20)?

Answer 1

Use the intercept form: `y = a(x-x_"r1")(x-x_"r2")`
where `x_"r1"` is the first x intercept and `x_"r2"` is the second.
The value of "a" is found by evaluating at the other point.
`99y=20x^2+360x+1600`

Explanation:

Begin with the intercept form:

`y = a(x-x_"r1")(x-x_"r2")`

Substitute in the intercepts:

`y = a(x-(-10))(x-(-8))" [1]"`

Evaluate at the point `(1,20)`:

`20 = a(1+10)(1+8)`

`a = 20/99`

Substitute the value for "a" into equation [1]:

`y = 20/99(x+10)(x+8)`

or `99y=20x^2+360x+1600`

graph{99y=20x^2+360x+1600 [-17.705, 2.295, -0.48, 9.52]}