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# 3.1 Notes - Remember that not all parabolas will have...

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Slide 1 Quadratic Functions College Algebra Section 3.1 Slide 2 Standard Form A function f is a quadratic function if f(x) = ax 2 + bx + c, where a, b, and c are real numbers with a ≠ 0. Slide 3 Important Features of a Parabola Vertex Axis of symmetry x-intercept(s) y-intercept Domain Range

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Slide 4 Vertex and Axis of Symmetry If the parabola is written in the form f(x) = a(x – h) 2 + k the vertex is at the point ( h,k ). If the parabola is written in the form f(x) = ax 2 + bx + c find the vertex using the fact that the x- coordinate is x = -b/2a . The axis of symmetry is always the vertical line x = -b/2a. Slide 5 Intercepts As always, find the x-intercept(s) by setting y = 0 and solving for x.
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Unformatted text preview: Remember that not all parabolas will have x-intercepts. If this is the case you will get complex numbers for solutions. Find the y-intercept by setting x = 0 and solving for y. You will always have exactly one y-intercept when graphing parabolas. In both cases, make sure you write your intercepts as ordered pairs . Slide 6 Applications The position function is one application of quadratic functions. Recall: s(t) = -16t 2 + v t + s Example: #48 Note that in applications where you are asked to find either a maximum or minimum value, you just need to find the vertex. Example: #54...
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