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# section21_material - Section 2.1 Quadratic Functions and...

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MATH 110 BUSINESS CALCULUS CHAPTER 2 NONLINEAR MODELS Section 2.1 Quadratic Functions and Models A quadratic function of variable x is a function that can be written in the form 2 () f xa xb x c = ++ where a , b , and c are fixed numbers ( 0 a ) A parabola is a graph of a quadratic function. If a > 0, the parabola opens upward (concave up) If a < 0, the parabola opens downward (concave down) In the picture, the parabola on the left is concave up, and the parabola on the right is concave down.

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Vertex: 0, 0 () xy 0 2 b x a =− 00 yf x = X-intercepts: set y = 0 2 0 ax bx c + += 2 4 2 bb a c x a −± = Y-intercept: set x = 0 2 (0) (0) y ab c c = ++ = The parabola is symmetric with respect to the vertical line passing through the vertex. This vertical line is called
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section21_material - Section 2.1 Quadratic Functions and...

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