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19 Cards in this Set
- Front
- Back
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Quadratic Function |
a nonlinear function that can be written in this standard form. |
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The graph of a quadratic takes on what shape? |
U - Shape. Called a parabola. |
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Vertex |
The vertex is the turning point of a quadratic or absolute value function |
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Axis of symmetry |
The vertical line that divides the parabola into two symmetric parts. |
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Graphing f(x) = ax^2 when a >0 |
When 0 < a < 1, the graph is a vertical shrink of the parent function.
When a > 1, the graph is a vertical stretch of the parent function. |
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Parent Function of a Quadratic |
F(x) = x^2 |
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Graphing f(x) = ax^2 when a < 0 |
When -1 < a < 0, the graph is a vertical shrink with a reflection over the x - axis. When a < -1, the graph is a vertical stretch with a reflection over the x - axis. |
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Graphing f(x) = x^2 + c |
When c > 0, the graph is a translation c units up. When c < 0, the graph is a translation c units down. |
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When is the graph of f(x) = ax^2 + bx + c opening up? (concave up) |
When a > 0 |
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When is the graph of f(x) = ax^2 + bx + c opening down? (concave down) |
When a < 0 |
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What is the y-intercept of f(x) = ax^2 + bx + c ? |
the value of c |
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What is the x-coordinate of the vertex of f(x) = ax^2 + bx + c ? |
-b/2a |
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What is the axis of symmetry of f(x) = ax^2 + bx + c ? |
x = -b/2a |
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Maximum Value |
the y-coordinate of the vertex of the graph f(x) = ax^2 + bx + c when a < 0. |
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Minimum Value |
the y-coordinate of the vertex of the graph f(x) = ax^2 + bx + c when a > 0. |
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Graphing f(x) = a(x - h)^2 |
When h > 0, the graph is a horizontal translation h units right. (this looks like subtraction) When h < 0, the graph is a horizontal translation h units left. ( this looks like addition) |
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Vertex Form |
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Intercept Form |
f(x) = a(x - p)(x - q) The x - intercepts are p and q. The axis of symmetry is x = (p + q)/2 The graph opens up what a > 0 and down when a < 0. |
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Zero |
An x-intercept or root. |
