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Question Completion Status:a) Sign of the leading coefficientb) Vertexc) Axis of symmetryd) Intervals where fis increasing and where fis decreasingf) Domain and range
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Q. Question Completion Status:a) Sign of the leading coefficientb) Vertexc) Axis of symmetryd) Intervals where fis increasing and where fis decreasingf) Domain and range
- Leading Coefficient Sign: a) To find the sign of the leading coefficient, look at the coefficient of in the function .If , the parabola opens upwards and the leading coefficient is positive.If , the parabola opens downwards and the leading coefficient is negative.
- Vertex Calculation: b) The vertex of a parabola given by is found using the formula . Calculate to find the -coordinate of the vertex. Then, substitute this value into the function to find the -coordinate.
- Axis of Symmetry: c) The axis of symmetry is a vertical line that passes through the vertex of the parabola.It has the equation .
- Function Increasing/Decreasing: d) The function is increasing on the interval where and decreasing where if . If , then is increasing where and decreasing where .
- Domain and Range: f) The domain of any quadratic function is all real numbers, or . The range depends on the sign of the leading coefficient and the vertex. If , the range is . If , the range is .
