Range
2x2=-32
x2=-16
x=±4i
(2x+1)(x+11)
y = 2(x - 0.5)(x - 5)
or
y = 2(2x - 1)(x - 5)
(x-12)(x+11)
y=-(x2+10x-2x-20)
y=-(x2+8x-20)
y=-x2-8x+20
y≥-2
x = ±7
(-4,6)
y=(x+4)(x+4)-1
y=x2+4x+4x+16-1
y=x2+8x+15
PARABOLA
By Vertex Formula:
x=-(-7)/(2*3)
7/6
or
1.1667
y=(x-2)2-9
From the vertex we know:
y=a(x-1)2-2
From the point we know x & y:
0=a(0-1)2-2
0=a(-1)2-2
0=1a-2
2=a
Put "a" in the equation
y=2(x-1)2-2
(x+3)2=25
√ both sides
x+3 = ±5
x=-3±5
x=-3+5=2 and x=-3-5=-8
x=2 and x = -8
Solve: 0=16x2-1
(1/4, 0) and (-1/4, 0)
(3x-2)(x+5)
AXIS OF SYMMETRY
y+c=(x2 -10x+c) +21
Find c: 1/2(10)=5→52=25=c
y+25 = (x2-10x+25)+21
y+25=(x-5)2+21
subtract 25 from both sides
y=(x-5)2-4
(x-3)(x-8)
VERTEX
x=-1/2 and x=3
(5x+2)(5x-2)
What is the vertex of the parabola?
y=-0.5(x+4)2+6
A parabola has a vertex of (1,-2) and passes through the point (0,0).
What is the equation of the parabola?
What is the equation in standard form?
y=(x+4)2-1
Factor the expression:
3x2+13x-10
Factor the expression:
x2-11x+24
What is the name of the line that cuts the graph of a quadratic in half?
Solve this equation:
(2x+1)(x-3)=0
What is the equation in standard form?
y=-(x-2)(x+10)
What is the vertex formula?
What is the name of the maximum or minimum of a quadratic function?
Solve this equation:
x2 = 49
Solve the equation:
2x2+6=-26
Factor the expression:
x2-x-132
What is the name of the graph of a quadratic function?
Solve this equation:
x2+6x+9=25
Factor the expression:
2x2+23x+11
Solve this equation:
0=2x2-7x-5
Given: a=1
What is the equation of the parabola in vertex form?
What is the range of this parabola?
What is the vertex form of the equation?
y=x2-10x+21
What are the coordinates of the x-intercepts of this quadratic function?
y=16x2 - 1
What is the Axis of Symmetry of this quadratic function?
y=3x2-7x
Given: One x-intercept is (0.5,0) and a = 2.
What is the equation of the quadratic function in intercept form?
Factor the expression:
25x2-4
What is the set of all possible y-values called?
Description | Match: |
What is the name of the graph of a quadratic function? | PARABOLA |
What is the name of the line that cuts the graph of a quadratic in half? | AXIS OF SYMMETRY |
What is the name of the maximum or minimum of a quadratic function? | VERTEX |
What is the vertex formula? | |
What is the set of all possible y-values called? | Range |
Solve this equation: x2 = 49 | x = ±7 |
Solve this equation: (2x+1)(x-3)=0 | x=-1/2 and x=3 |
Solve the equation: 2x2+6=-26 | 2x2=-32 x2=-16 x=±4i |
Solve this equation: x2+6x+9=25
| (x+3)2=25 √ both sides x+3 = ±5 x=-3±5 x=-3+5=2 and x=-3-5=-8 x=2 and x = -8 |
Solve this equation: 0=2x2-7x-5 | |
Factor the expression: x2-11x+24 | (x-3)(x-8) |
Factor the expression: x2-x-132 | (x-12)(x+11) |
Factor the expression: 25x2-4 | (5x+2)(5x-2) |
Factor the expression: 2x2+23x+11 | (2x+1)(x+11) |
Factor the expression: 3x2+13x-10 | (3x-2)(x+5) |
What is the vertex of the parabola? y=-0.5(x+4)2+6 | (-4,6) |
Given: a=1 What is the equation of the parabola in vertex form? | y=(x-2)2-9 |
Given: One x-intercept is (0.5,0) and a = 2. What is the equation of the quadratic function in intercept form?
| y = 2(x - 0.5)(x - 5) or y = 2(2x - 1)(x - 5) |
What are the coordinates of the x-intercepts of this quadratic function? y=16x2 - 1 | Solve: 0=16x2-1 (1/4, 0) and (-1/4, 0) |
What is the Axis of Symmetry of this quadratic function? y=3x2-7x | By Vertex Formula: x=-(-7)/(2*3) 7/6 or 1.1667 |
What is the range of this parabola? | y≥-2 |
What is the equation in standard form? y=(x+4)2-1 | y=(x+4)(x+4)-1 y=x2+4x+4x+16-1 y=x2+8x+15 |
What is the equation in standard form? y=-(x-2)(x+10) | y=-(x2+10x-2x-20) y=-(x2+8x-20) y=-x2-8x+20 |
What is the vertex form of the equation? y=x2-10x+21 | y+c=(x2 -10x+c) +21 Find c: 1/2(10)=5→52=25=c y+25 = (x2-10x+25)+21 y+25=(x-5)2+21 subtract 25 from both sides y=(x-5)2-4 |
A parabola has a vertex of (1,-2) and passes through the point (0,0). What is the equation of the parabola? | From the vertex we know: y=a(x-1)2-2 From the point we know x & y: 0=a(0-1)2-2 0=a(-1)2-2 0=1a-2 2=a Put "a" in the equation y=2(x-1)2-2 |