Quadratic Functions Application Thinking Test MCR3U Unit 3

Q1. Find inverse of f(x) = -4(x + 1)2 + 6.
State restriction on f(x) to ensure inverse to be a function.
Determine domain of f(x) when range is y  2.

Q2. If f(x) = 3x2 + (k – 1)x + 12 has one zero, find k.

Q3. Determine the equation of parabola with x-intercepts , with a y-intercept 2.

Q4. Given y = 4 – x2 and x + y = 2. Determine the point(s) of intersection. Answer in radical form.

Q5. Find the value of k that makes x2 + (k + 7)x + (7k + 1) a perfect square.

Q6. A toy store owner sells a $ 45 toy which results in annual sales of 3000 units. The store owner estimates that each $2 increase in selling price will decrease sales by 125 units. Also, the toy costs the store owner $17 each from the toy manufacturer. Find the selling price of the toy which will maximize the owner’s profits.

Q7. You are given a square-root function, and asked to find the equation of the inverse. Explain clearly the steps you’d take to find the equation and how you’d adjust the equation.

Q8. For a function in the form f(x) = a(x – p)2 + q, how would one use the values of a and q to find the number of zeros?