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Unformatted text preview: 43: 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 yintercept
is (0, c); the xintercept is (x, 0). The determinant, b2 – 4ac, is used to find the number of xintercepts. If b2 – 4ac > 0, there are two xintercepts; if it is = 0, there is one; and if < 0, there
are none. If it has xintercepts, 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 yint. xint. 3. f(x) = x2 – 2x – 3
Up/Down Vertex Axis of Sym yint. 12
x − 2x − 5
3 Up/Down Vertex Axis of Sym yint. xint. 4. f(x) = 3x2 – 8x + 2
xint. Up/Down Vertex Axis of Sym yint. xint. 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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 Fall '08
 Staff
 Completing The Square, Real Numbers, Transformations, Quadratic equation, Cliff, 45°, 400 ft, 500 ft, ft/sec.

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