Quadratic Functions and their Graphs
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
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| If a>0, the graph of the quadratic function opens which way? | Upward
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| If a<0, the graph of the quadratic function opens which way? | Downward
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| The vertex of a parabola defined by f(x)=a(x-h)^2+k has a vertex defined by the values of which variables? | (h,k)
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| What is the vertex of the quadratic function g(x)= (x-4)^2-2? | (4,2)
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| What is the vertex of the quadratic function f(x)= 3(x-8)+6? | (8,6)
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| In the equation f(x)=(x-2)+6, is h positive or negative? | Positive
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| In the equation f(x)=(x+9)+3, is h positive or negative? | Negative
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| In graphs with the equation f(x)=x^2+k, what happens to the graph when k is negative? | The graph will shift |k| downward from y=x^2
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| In graphs with the equation f(x)=x^2+k, what happens to the graph when k is positive? | The graph will shift |k| upward from y=x^2
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| In graphs with the equation f(x)=(x-h)^2, what happens to the graph when h is positive? | The graph will shift h units to the right from y=x^2
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| In graphs with the equation f(x)=(x-h)^2, what happens to the graph when h is negative? | The graph will shift h units to the left from y=x^2
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| What is another name for the vertex (h,0)? | The x-intercept
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| What is another name for the vertex (0,k)? | The y-intercept
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| In a parabola defined by f(x)=a(x-h)^2+k, when the absolute value of a is greater than 1, how does the graph compare to the graph of y=x^2? | The graph is narrower than y=x^2
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| In a parabola defined by f(x)=a(x-h)^2+k, when the absolute value of a is less than 1, how does the graph compare to the graph of y=x^2? | The graph is wider than y=x^2
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| How do you determine a parabola's axis of symmetry? | The axis of symmetry is the same as the value of h; if h=4, then the axis of symmetry is x=4
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| For f(x)=x^2+2, state the vertex, axis of symmetry, and whether the parabola opens upward or downward. | (0,2), x=0, downward
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| The graph of f(x)=ax^2+bx+c when a is not 0 is a parabola with a vertex of what? | (-b/2a, f(-b/2a))
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| How do you solve an equation by completing the square? | Add the square of half the coefficient of x, and then use the square root property to get two solutions.
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| Make a perfect square trinomial from x^2+12x | x^2+12x+36
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