Making up an Equation Satisfies Given Conditions

[Joystar77]

Make up an equation that satisfies the given conditions: must have x-intercepts at (-1, 0) and (2, 0). It must also have a y-intercept at (0, 4).

Is this the correct way for this equation of x-intercepts would look like?

y = (x - 2) (x + 1)

How do you factor the y-intercept?

 

[JeffM]

Make up an equation that satisfies the given conditions: must have x-intercepts at (-1, 0) and (2, 0). It must also have a y-intercept at (0, 4).

Is this the correct way for this equation of x-intercepts would look like?

y = (x - 2) (x + 1)

How do you factor the y-intercept?

You are very much thinking straight, but you missed one little piece of the puzzle.

If f(x) is a polynomial of degree n and f(2) = 0 = f(- 1), then, by the zero product property and the fundamental theorem of algebra, f(x) = g(x) * (x - 2)(x + 1), where g(x) is a polynomial of
degree n - 2.

\(\displaystyle n = 2 \implies g(x) = ax^{(n - 2)} = ax^0 = a.\)

In other words, \(\displaystyle y = a(x - 2)(x + 1) = a(x^2 - x - 2) = ax^2 - ax - 2a.\)

What does it mean if f(x) has a y intercept of 4?

Can you now figure out what a equals?