Quadratic & Rational Functions Flashcards
What is the definition of a quadratic function?
What is the shape of a quadratic?
A parabola
What does the a value tell you in f(x)= ax² + bx+ c?
The direction of the parabola
What happens if a>0 or a<0?
Every parabola has… (3)
Find the zeros of f(x)= 2x² + 12x + 17
x = -3 + 1/2√2
x = -3 - 1/2√2
Find the axis of symmetry and vertex of f(x)= 2x² + 12x + 17.
What is a polynomial?
Expression consisting of indeterminates and coefficients, that involve only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
What is the form of a polynomial?
What is a rational function?
What is a vertical asymptote?
Vertical line x=a where y approaches +/- infinity.
What is a horizontal asymptote?
Horizontal line y =b approaches as x goes to +/- infinity
Find the VA, HA, x-intercept, hole of discontinuity, x-intercept, and y-intercept of :
Find the vertex, the VA and HA: y(x) = 2x² + 10x +12
Find the vertex, the VA, and HA: f(x) = 2x² - 10x +4
Find the vertex, the VA, and HA:
h(t) = -4t² + 6t -4
Rewrite the quadratic function into vertex form:
f(x) = x² - 12x +32
Rewrite the quadratic function into vertex form:
f(x) = 2x² +8x -10
Find the values of b and c so f (x)= -8x² +bx +c has vertex (2,-7)
Write an equation for a quadratic with the given features: x-intercepts (-3, 0) and (1, 0), and y intercept (0, 2)
Write an equation for a quadratic with the given features: x-intercepts (2, 0) and (5, 0), and y intercept (0, 6)
Write an equation for a quadratic with the given features: Vertex at (4, 0), and y-intercept (0, -4)
Write an equation for a quadratic with the given features: Vertex at (-3, 2), and passing through (3, -2)
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?
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?
For each function, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal asymptotes. Use that information to sketch a graph.
For each function, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal asymptotes. Use that information to sketch a graph.
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)
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
Write an equation for a rational function with the given characteristics.
Vertical asymptote at x = -1 Double zero at x = 2
Write an equation for the rational functions graphed.
Write an equation for a rational function graphed.
