4.3 Quadratic Functions

4.3 Quadratic Functions - 4-3: Quadratic Functions A...

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Unformatted text preview: 4-3: Quadratic Functions A quadratic function has the form f(x) = ax2 + bx + c, where a, b, and c are real numbers and a ≠ 0. In order to graph a quadratic function using transformations, by completing the square the function can be rewritten in the form of f(x) = a(x – h)2 + k, where (h, k) is the vertex. They can also be graphed using the vertex, axis of symmetry, and intercepts. The y-intercept is (0, c); the x-intercept is (x, 0). The determinant, b2 – 4ac, is used to find the number of xintercepts. If b2 – 4ac > 0, there are two x-intercepts; if it is = 0, there is one; and if < 0, there are none. If it has x-intercepts, quadratic formula may be used to find them. Graph the quadratic function by determining whether the graph opens up or down and by finding its vertex, axis of symmetry 2. Graph: f ( x ) = 1. Graph: f(x) = -2x2 + 8x - 6 Up/Down Vertex Axis of Sym y-int. x-int. 3. f(x) = x2 – 2x – 3 Up/Down Vertex Axis of Sym y-int. 12 x − 2x − 5 3 Up/Down Vertex Axis of Sym y-int. x-int. 4. f(x) = 3x2 – 8x + 2 x-int. Up/Down Vertex Axis of Sym y-int. x-int. 5. The height h of a projectile fired at a 45° angle from an altitude a at an initial velocity of v ft/sec. is given by the is given by h( x ) = −32 x 2 + x + a . If a projectile is fired from a 400 ft v2 cliff with a muzzle velocity of 500 ft/sec., find [a] its maximum height and [b] where it will strike the ground. Graph the function. [a] [b] [c] 6. The graph of the function f(x) = ax2 + bx +c has vertex at (1, 4) and passes through the point (­1, ­8). Find a, b, and c. ...
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This note was uploaded on 01/04/2012 for the course MAC 1105 taught by Professor Staff during the Fall '08 term at Miami Dade College, Miami.

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4.3 Quadratic Functions - 4-3: Quadratic Functions A...

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