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| What is the quadratic function in vertex form and how can this be used to find the vertex of its respective graph? |
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| What is the quadratic function in factored form and how can you find the line of symmetry with this function? |
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| What is the quadratic formula in standard form and how do we find the line of symmetry? |
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| Optimization is finding the minimum or maximum of a (quadratic) function. |
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| What is the range of a function? |
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Range: the possible output (y) values for a function.
e.g. For f(x) = x2 no matter what value of x is used as an input, the output values are either positive or zero (because a negative # squared is positive). Hence (for this example!) the range is all numbers greater than or equal to 0. |
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What are the ways of solving a quadratic function? |
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- Factoring
- Using the GDC
- Square root principle
- Completing the square
- Quadratic formula
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| What is the discriminant? |
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[image]
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It tells us the nature of the root.
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If the answer is >0 then there are 2 real roots
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If the answer is = 0 then there is 1 real root (the vertex touch the x-axis)
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If the answer is <0 then it has 2 non-real roots
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| What is the quadratic formula? |
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| What is the necessary condition of a quadratic function in order to use the "completing the square" method to solve it? |
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| The leading coefficent must be 1. |
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solve using factorizing:
[image] |
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[image]
Therefore,
[image] |
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What is the function of this graph in vertex form?
(hint: a=1)
[image] |
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| What is the midpoint formula? |
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| What is the distance formula for 2 dimensions? 3 dimensions? |
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| Use the square root principle to solve the following:[image] |
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