A parabola with labeled -intercepts suggests factored form: each intercept makes one factor zero. Use a point off the -axis to find the multiplier with a Desmos regression, which fits an unknown number. Watch the sign inside each factor: a negative zero needs a plus sign. The zeros alone cannot determine the multiplier.
Hints
- Hint 1
An -intercept is where the graph has output . In factored form, each such input makes one factor zero. What factors become zero at the two labeled intercepts?
- Hint 2
Use the point on the -axis, where . A graph point says , so this point gives an equation for the multiplier that the -intercepts cannot determine.
Step-by-step
Use the intercepts to build factored form
Step 1Write the factors from the zeros
The labeled -intercepts are and . Their inputs are the zeros, where the output is , so use factors that vanish at those inputs:
Here is the unknown multiplier. Don't use for the left intercept: that factor vanishes at , not .
- Step 2
Turn the other marked point into an equation
The -intercept is where . Its label says , so substitute into the factored form:
Don't use either zero to find : at a zero, the product is regardless of the multiplier.
- Step 3
Find the multiplier and identify the function
Type . The tells Desmos to fit the unknown multiplier . Under PARAMETERS, it shows , which equals . So the equation is , with both marked zeros and the marked -intercept. Choice A.