Quadratic Graphs

This is the graph of y = x² + bx + 4. What is b?

• 2

• 4

• -2

• -4

Answer explanation

vertex = (-2,0) so h=-2, but h = (-b)/2a

It is given that ax² + 8x + 16 touches the x-axis at one point. Find the value of a.

• 1

• 2

• 3

• 4

Answer explanation

Discriminant = b² - 4ac = 0

What is the minimum or maximum of x² - 4x + 7?

• minimum value = 7

• minimum value = 3

• maximum value = 7

• maximum value = 3

Answer explanation

Can be transformed to (x-2)² + 3

What is the maximum or minimum value of

 $-x^2+2x+6$  ?

• Maximum value = 6

• Maximum value = 7

• Minimum value = 6

• Minimum value = 7

Answer explanation

The expression can be transformed to  $-\left(x-1\right)^2+7$    

The quadratic equation x² - 7x + 6 = 0 has

• No real roots

• One repeated root

• Two distinct and integral roots

• Two distinct real roots, but the roots are irrational numbers

Answer explanation

Discriminant = 7² - 4(1)(6) = 25, it is a perfect square

The quadratic equation x² - 8x + 2 = 0 has

• No real roots

• Two equal real roots

• Two distinct and integral roots

• Two distinct roots but the roots are irrational numbers.

Answer explanation

Discriminant = 8² 4(1)(2) = 56 which is not a perfect square.

The roots of x² - 7x + 12 = 0 are

• 2, 3

• 3, 4

• 2, 6

• 1, 12

Answer explanation

x² - 7x + 12 = (x-3)(x-4)

The equation of the graph is y = -x²+ 2x + 6. The axis of symmetry of the graph is

• x=1

• y=1

• x=2

• y=6

Answer explanation

The axis of symmetry is x=h, where h = -b/(2a)

Which of the following line does not intersect with the graph y = -x² + 2x + 6 ?

• y=5

• x=1000

• y=8

• x=1

Answer explanation

The maximum point is (1,7)

The y-intercept of the graph y = (x-2)² - 2 is

• -2

• 2

• 1

• -1

Answer explanation

put x = 0, y = 2