Quadratic functions

Question 1

domain of a quadratic function

Answer 1

(–∞, ∞)

Question 2

general form of a quadratic function

Answer 2

f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0

Question 3

standard form of a quadratic function

Answer 3

f(x) = a(x – h)² + k, where a, h, and k are real numbers and a ≠ 0

Question 4

vertex of a quadratic function in standard form

Answer 4

(h, k)

Question 5

axis of symmetry of a parabola

Answer 5

the vertical line through the vertex, x = h

Question 6

a parabola opens upwards when

Answer 6

a > 0

Question 7

a parabola opens downwards when

Answer 7

a < 0

Question 8

vertex of a quadratic function in general form

Answer 8

(–b/2a, f(–b/2a)

Question 9

the quadratic formula

Answer 9

x = [–b ± √(b² – 4ac)]/2a

Question 10

discriminant of a quadratic equation

Answer 10

b² – 4ac

Question 11

if b² – 4ac < 0,

Answer 11

the quadratic equation has no real solutions

Question 12

if b² – 4ac = 0

Answer 12

the quadratic has exactly one real solution

Question 13

if b² – 4ac > 0

Answer 13

the quadratic has exactly two real solutions

Question 14

if b² – 4ac > 0

Answer 14

the quadratic has exactly two real solutions

Question 15

graphical interpretation of the solutions to f(x) = g(x)

Answer 15

the solutions are the x values where the graphs of y = f(x) and y = g(x) intersect

Question 16

graphical interpretation of the solutions to f(x) < g(x)

Answer 16

the solution is the set of x values where the graph of y = f(x) is below the graph of y = g(x)

Question 17

graphical interpretation of the solutions to f(x) > g(x)

Answer 17

the solution is the set of x values where the graph of y = f(x) is above the graph of y = g(x)

Question 18

steps to solving a quadratic inequality

Answer 18

1. Rewrite the inequality as a quadratic function f(x) on one side and 0 on the other
2. Find the zeros of f and place them on the number line with the number 0 above them
3. Choose a real number, called a test value, in each of the intervals determined in step 2
4. Determine the sign of f(x) for each test value in step 3, and write that sign above the corresponding interval
5. Choose the intervals which correspond to the correct sign to solve the inequality