USING DISCRIMINANT TO FIND NUMBER OF SOLUTIONS WORKSHEET

Find the value of the discriminant to determine the number of zeros of each quadratic function.

Problem 1 :

f(x) = 2x² - 3x - 5

Solution

Problem 2 :

f(x) = 4x² + 4x + 1

Solution

Problem 3 :

f(x) = -5x² + x - 2

Solution

Problem 4 :

Determine the value of k so that the quadratic function

f(x) = x² - kx + 3

has only one zero.

Solution

Problem 5 :

For what values of k will the function 

f(x) = 3x² - 4x + k

have one x-intercept ?

Solution

Problem 6 :

For what values of k will the function 

f(x) = kx² - 4x + k

have no zero ?

Solution

Problem 7 :

The graph of the function

f(x) = x² - kx + (k + 8)

touches the x-axis at one point. what are the possible values of k ?

Solution

Problem 8 :

If f(x) = x² - 6x + 14 and g(x) = -x² - 20x - k

determine the value of k so that there is exactly one point of intersection between the two parabolas.

Solution