3A7 Roots of Quadratic Equations

What is the expression for the discriminant of a quadratic function?

• b² + 4ac

• b² - 4bc

• b² - 4ac

• b² + 4bc

What is the minimum point of the quadratic function

y = (x - 2)² + 3

• (-2 , 3)

• (2 , -3)

• (-2 , -3)

• (2 , 3)

Determine the nature of roots for the following equation

y = 2x² - x + 1

• two real and distinct roots

• two real and equal roots

• two real roots

• no real roots

What are the conditions required for

ax² + bx + c to be

always positive?

• a > 0 and b² - 4ac < 0

• a > 0 and b² - 4ac > 0

• a < 0 and b² - 4ac < 0

• a < 0 and b² - 4ac > 0

State the maximum value of

-2(x + 3)² - 17

• -3

• -6

• -17

• -34

State the coordinates of the turning point of the graph y = 2x² - 12x + 10

• (2 , -6)

• (3 , -8)

• (6 , 10)

• (-1, 24)

Find the value of k for which the equation 2x² - 4x + k has two real and equal roots.

• k = -2

• k = 2

• k = -1

• k = 1