grade 11 applied math

Question

A parabola has a vertex of (4, 8) and points down.

Write two possible equations of quadratic functions in vertex form such that the parabola has exactly two zeroes.

Find the zeroes for both functions.

Marks may be awarded as outlined below. If your teacher plans to use a different strategy to evaluate your work they will inform you before you start the assignment.
Unless you are instructed differently this assignment is worth 6 marks. Use the following information to guide your work:

1 mark for setting up the first function with the vertex substituted appropriately
1 mark for choosing an appropriate a value for the first function
1 mark for finding both the zeroes for the first function
1 mark for setting up the second function with the vertex substituted appropriately
1 mark for choosing an appropriate a value for the second function
1 mark for finding both the zeroes for the second function

Answer 1

y(x) = a(x-4)^2 + 8; a < 0; or

 

1.  y(x) = a(x - 1)(x -7);  then:   y(4) = a(4 -1)(4 - 7) = a(3)(-3) = -9a = 8;   or,   y = -(8/9)(x-4)^2 + 8

 

2. y(x) = a(x - 2)(x - 6);  then:   y(4) = a(4 - 2)(4 - 6) = a(2)(-2) = -4a = 8;  or,   y = -2(x-4)^2 + 8