Unit 11 · Quadratic Functions
Standard form ax² + bx + c, vertex form a(x − h)² + k, and factored form a(x − r)(x − s) highlight different features of the same parabola.
Standard: y-intercept c, and axis x = −b/(2a). Vertex: vertex (h, k) and stretch a. Factored: x-intercepts r and s. The axis of symmetry is midway between the roots.
If a > 0 the parabola opens up (minimum). If a < 0 it opens down (maximum).
The turning point of a parabola; a maximum or a minimum.
Example: For y = (x − 3)² + 1, the vertex is (3, 1).
The vertical line through the vertex that splits the parabola into mirror images.
Example: For vertex (3, 1), the axis is x = 3.
The x-intercepts of the graph; solutions of f(x) = 0.
Example: y = (x − 2)(x + 5) has roots 2 and −5.
Try the prompt first. The steps stay folded until you ask to see them.
For f(x) = −2(x + 1)² + 8, state the vertex, axis, direction, and y-intercept.
Watch for
Reading (x + 1) as h = +1
Vertex form is (x − h), so x + 1 = x − (−1).
Fix: Rewrite as (x − (negative number)).
Submit each answer to check it. The key is not shown until you do.
A ball was launched into the air, and its height above the ground was recorded each second: Time (sec): 0, 1, 2, 3, 4 Height (ft): 11, 59, 75, 59, 11 Based on these data, which statement is a valid conclusion?
The students in Mrs. Smith’s algebra class were asked to describe the graph of g(x) = 2(x − 3)² compared to the graph of f(x) = x². Which student response is correct?
A ball was launched into the air, and its height above the ground was recorded each second: Time (sec): 0, 1, 2, 3, 4 Height (ft): 11, 59, 75, 59, 11 Based on these data, which statement is a valid conclusion?
Use the quadratic applet and match sliders to each form.
Complete the square for x² + 6x + 5 to reveal the vertex.
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