11QuadraticEquations Flashcards
What is a parabola?
It is a curve whose every point is equidistant between a point and a line (directrix)
What is the equation for a parabola?
What are a and c?
What general info do you get from b?
y = ax² + bx + c
a gives direction and tightness
c gives y-intercept
b points the direction of the vertex. The smaller b, the more the graph moves to the right.
The vertex of a parabola peaks when b = 0.
What are the coordinates of the vertex in:
ax² + bx + c = y
ax² + bx + c = y
the x-coordinate is -b/2a
This comes from the Quadratic equation:
the y-coordinate is determined by plugging the x-coordinate in
What is the vertex of:
x² + 3x + 1 = y
-3/2, -5/4
How do you find the x-intercepts of a quadratic equation?
The roots of the equation.
What are the x-intercepts of
x² + 4x +4 = y
(x + 2)²
one intercept → -2
Give the y-intercept, vertex of:
g(x) = x² + 3
g(x) = x² + 3
y-intercept = 3
since it faces up, there are no x-intercepts
The vertex is (0, 3)
What are the y-intercept, vertex and x-intercepts of
h(x) = (x - 2)²
h(x) = (x - 2)²
h(x) = x² -4x + 4
y-intercept = 4
vertex = (2, 0)
x-intercept = 2,0
What are the y-intercept, vertex and x-intercepts of
f(x) = (x + 1)² - 4
f(x) = (x + 1)² - 4
f(x) = x² + 2x - 3
a = 1; b = 2; c = -3
y-intercept = -3
(x + 3)(x - 1)
x-intercepts = -3 and 1
-b/2a x-vertex = -2/2 = -1
vertex = (-1, -4)
What is the vertex of
f(x) = x² - 5
f(x) = x² - 5
a = 1; b = 0, c = -5
vertex = 0, -5
What is the vertex of
f(x) = (x - 4)²
f(x) = (x - 4)²
f(x) = x² - 4x + 16
a = 1; b = -4; c = 16
vertex = 4, 0
What is the vertex of
f(x) = (x + 1)²
f(x) = (x + 1)²
f(x) = x² + 2x + 1
a = 1; b = 2; c = 1
vertex = -1, 0
