Quadratic & Rational Functions

Question 1

What is the definition of a quadratic function?

Answer 1

Question 2

What is the shape of a quadratic?

Answer 2

A parabola

Question 3

What does the a value tell you in f(x)= ax² + bx+ c?

Answer 3

The direction of the parabola

Question 4

What happens if a>0 or a<0?

Answer 4

Question 5

Every parabola has… (3)

Answer 5

Question 6

Find the zeros of f(x)= 2x² + 12x + 17

Answer 6

x = -3 + 1/2√2
x = -3 - 1/2√2

Question 7

Find the axis of symmetry and vertex of f(x)= 2x² + 12x + 17.

Answer 7

Question 8

What is a polynomial?

Answer 8

Expression consisting of indeterminates and coefficients, that involve only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Question 9

What is the form of a polynomial?

Answer 9

Question 10

What is a rational function?

Answer 10

Question 11

What is a vertical asymptote?

Answer 11

Vertical line x=a where y approaches +/- infinity.

Question 12

What is a horizontal asymptote?

Answer 12

Horizontal line y =b approaches as x goes to +/- infinity

Question 13

Find the VA, HA, x-intercept, hole of discontinuity, x-intercept, and y-intercept of :

Answer 13

Question 14

Find the vertex, the VA and HA: y(x) = 2x² + 10x +12

Question 15

Find the vertex, the VA, and HA: f(x) = 2x² - 10x +4

Question 16

Find the vertex, the VA, and HA:
h(t) = -4t² + 6t -4

Question 17

Rewrite the quadratic function into vertex form:
f(x) = x² - 12x +32

Question 18

Rewrite the quadratic function into vertex form:
f(x) = 2x² +8x -10

Question 19

Find the values of b and c so f (x)= -8x² +bx +c has vertex (2,-7)

Question 20

Write an equation for a quadratic with the given features: x-intercepts (-3, 0) and (1, 0), and y intercept (0, 2)

Question 21

Write an equation for a quadratic with the given features: x-intercepts (2, 0) and (5, 0), and y intercept (0, 6)

Question 22

Write an equation for a quadratic with the given features: Vertex at (4, 0), and y-intercept (0, -4)

Question 23

Write an equation for a quadratic with the given features: Vertex at (-3, 2), and passing through (3, -2)

Question 24

A rocket is launched in the air. Its height, in meters above sea level, as a function of time, in seconds, is given by h(t) = -4.9t² +229t +234.

a. From what height was the rocket launched?
b. How high above sea level does the rocket reach its peak?
c. Assuming the rocket will splash down in the ocean, at what time does
splashdown occur?

Answer 24

The height of a ball thrown in the air is given by h(x) = x²/12 +6x+3, where x is the horizontal distance in feet from the point at which the ball is thrown.

a. How high is the ball when it was thrown?
b. What is the maximum height of the ball?
c. How far from the thrower does the ball strike the ground?

Question 25

Question 26

For each function, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal asymptotes. Use that information to sketch a graph.

Question 27

For each function, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal asymptotes. Use that information to sketch a graph.

Question 28

Write an equation for a rational function with the given characteristics.
Vertical asymptotes at x = 5 and x = -5
x-intercepts at (2,0) and (-1,0).
y-intercept at (0,4)

Answer 28

Question 29

Write an equation for a rational function with the given characteristics.

Vertical asymptotes at x =-4 and x =-5
x-intercepts at (4,0) and (-6,0)
Horizontal asymptote at y = 7

Answer 29

Question 30

Write an equation for a rational function with the given characteristics.
Vertical asymptote at x = -1 Double zero at x = 2

Answer 30

Question 31

Write an equation for the rational functions graphed.

Answer 31

Question 32

Write an equation for a rational function graphed.

Answer 32

Question 33

Answer 33