Quadratic Function Quiz 3 MCR3U Solved Paper Standard Vertex and Factored Form

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Standard to Vertex Form
Q1. Consider the function, f(x) = -0.5(x + 3)2 + 8
a. Graph the function
b. Express f(x) in standard form

Q2. Consider the function, f(x) = 0.5(x – 6)(x + 4)
a. Graph the function
b. Express f(x) in standard form

Q3. An ice-cream company varies thr prices of its pint containers to maximize profit. The function P(x) = -75x2 + 300x – 200 models the company’s profits in thousands of dollars, where x is the price of a pint of ice-cream in dollars. At what price will the company receive maximum profits? How much profit will the company earn?

Q4. Anil threw a ball from 1 m above the ground. The ball reached a maximum height of 46 m at 3 seconds. Determine the equation that will model the parabola for this situation.

Q5. Harpreet has 120 m of fencing to enclose a rectangular pen for children’s play area. Determine a function to represent the area based on length of the rectangle. Determine the measurements for the dimensions of the rectangle with maximum area.

Q6. Find the value of k if the following function is quadratic.
Then write the equation in vertex form.

x -1 0 1 2 3
y -10 -20 -26 k 26