Essential Questions & Standards:
1. We will identify key features of a quadratic graph and sketch a graph based on the key features. MAFS.912.F-IF.2.4
2. We will determine if the function is quadratic based on a table, intercepts, and a vertex. MAFS.912.F-IF.3.8
3. We will graph a quadratic equation using vertex form and other key features. MAFS.912.F-IF.3.7, MAFS.912.A.REI.2.4
4. We will determine how quadratic functions transform on the dependent and independent variables. MAFS.912.F-BF.2.3
5. We will determine the zeros of a polynomial function. MAFS.912.A-APR.2.3
6. We will determine the end behavior of a polynomial function. MAFS.912.F-IF.3.7.c
7. We will determine how to graph polynomial functions. MAFS.912.F-IF.3.7
2. We will determine if the function is quadratic based on a table, intercepts, and a vertex. MAFS.912.F-IF.3.8
3. We will graph a quadratic equation using vertex form and other key features. MAFS.912.F-IF.3.7, MAFS.912.A.REI.2.4
4. We will determine how quadratic functions transform on the dependent and independent variables. MAFS.912.F-BF.2.3
5. We will determine the zeros of a polynomial function. MAFS.912.A-APR.2.3
6. We will determine the end behavior of a polynomial function. MAFS.912.F-IF.3.7.c
7. We will determine how to graph polynomial functions. MAFS.912.F-IF.3.7
Video 1: We will identify key features of a quadratic graph and sketch a graph based on the key features.
The two images above show important vocabulary and examples. Your (h,k) , aka vertex, shows if your paraphrase contains a minimum or maximum. The "a" tells us if your paraphrase opens up or down and how wide or narrow the parabola is. Vertex form is shown as f(x)= a (x-h) +k.
Video 2: We will determine if the function is quadratic based on a table, intercepts, and a vertex.
There are 5 steps in solving a quadratic equation with two solutions by graphing. First, you find the axis of symmetry. Second, find the vertex. Third, you create a table. Next, you find the zeros and finally you graph them.
Video 3: We will graph a quadratic equation using vertex form and other key features.
There are 6 steps in converting a quadratic from standard form to vertex form. These include:
Find the goal
Subtract
Find C
Add C
Factor
Subtract
Finally you'll have an ordered pair, also known as your vertex, for the solution.
Find the goal
Subtract
Find C
Add C
Factor
Subtract
Finally you'll have an ordered pair, also known as your vertex, for the solution.
The two images above show how to use vertex form and what the coefficient A does. They also provide an example problem.
Video 4: We will determine how quadratic functions transform on the dependant and independent variables.
- Positive coefficient - parabola opens up
- Negative coefficient - parabola opens down
- A>1 - narrow parabola
- 0 < a < 1 - wide parabola
f (x) is changing based on vertical shifts and vertical compression/ stretch.
Video 5: We will determine the zeros of a polynomial function.
The zeros of a polynomial function are the x intercepts. The x-intercept is the point where the graph of the line crosses the x-axis.
This image shows a good example of finding the zeros of a polynomial function. On the graph where I plotted three dots is the x intercepts, aka zeros.
Video 6: We will determine the end behavior of a polynomial function.
The end behavior of a polynomial function is the behavior of the graph of f(x) as x is either positive or negative infinity. The degree and the leading coefficient (a) of a polynomial function determine the end behavior of the graph.
Video 7: We will determine how to graph polynomial functions.
This example shows what two graphs could look like. If a graph is even then the end behavior shows both ends facing the same direction. When you have a graph that is negative and even, both ends face down. When your graph is positive and even, both ends face up.
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This is another example of two graphs. Unlike the even examples, polynomials with odd end behavior face different directions. If your graph is positive and odd, the first end faces down and the second one goes upward. If the graph is negative and odd, the first end faces up and the second one goes downward.
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