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Module 19

Quadratic Functions and their Graphs

QuestionAnswer
If a>0, the graph of the quadratic function opens which way? Upward
If a<0, the graph of the quadratic function opens which way? Downward
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)
What is the vertex of the quadratic function g(x)= (x-4)^2-2? (4,2)
What is the vertex of the quadratic function f(x)= 3(x-8)+6? (8,6)
In the equation f(x)=(x-2)+6, is h positive or negative? Positive
In the equation f(x)=(x+9)+3, is h positive or negative? Negative
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
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
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
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
What is another name for the vertex (h,0)? The x-intercept
What is another name for the vertex (0,k)? The y-intercept
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
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
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
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
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))
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.
Make a perfect square trinomial from x^2+12x x^2+12x+36