| Quadratic Vocabulary | ||
| #1 | What is the name of the graph of a quadratic function? |
PARABOLA |
| #2 | What is the name of the line that cuts the graph of a quadratic in half? |
AXIS OF SYMMETRY |
| #3 | What is the name of the maximum or minimum of a quadratic function? |
VERTEX |
| #4 | What is the vertex formula? |
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| #5 | What is the set of all possible y-values called? |
Range |
| Solving Quadratic Equations | ||
| #1 | Solve this equation: x2 = 49 |
x = ±7 |
| #2 | Solve this equation: (2x+1)(x-3)=0 |
x=-1/2 and x=3 |
| #3 | Solve the equation: 2x2+6=-26 |
2x2=-32 x2=-16 x=±4i |
| #4 | Solve this equation: x2+6x+9=25
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(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 |
| #5 | Solve this equation: 0=2x2-7x-5 |
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| Factoring | ||
| #1 | Factor the expression: x2-11x+24 |
(x-3)(x-8) |
| #2 | Factor the expression: x2-x-132 |
(x-12)(x+11) |
| #3 | Factor the expression: 25x2-4 |
(5x+2)(5x-2) |
| #4 | Factor the expression: 2x2+23x+11 |
(2x+1)(x+11) |
| #5 | Factor the expression: 3x2+13x-10 |
(3x-2)(x+5) |
| Graphing Quadratic Functions | ||
| #1 | What is the vertex of the parabola? y=-0.5(x+4)2+6 |
(-4,6) |
| #2 | Given: a=1 What is the equation of the parabola in vertex form?
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y=(x-2)2-9 |
| #3 | Given: One x-intercept is (0.5,0) and a = 2. What is the equation of the quadratic function in intercept form?
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y = 2(x - 0.5)(x - 5) or y = 2(2x - 1)(x - 5) |
| #4 | 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) |
| #5 | 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 |
| Random Quadratic Questions | ||
| #1 | What is the range of this parabola? |
y≥-2 |
| #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 |
| #3 | 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 |
| #4 | 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 |
| #5 | 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 |
| Final Question | |
Write an equation in vertex form that has a range of y≤5. |
Answers Vary. Any parabola with a y-coordinate of the vertex of 5 and opens down. |
