Graphing+Quadratic+Functions-Target+D-Converting+Forms+of+a+Quad-Guided+Learning

Target D: Convert a quadratic function into a different form to identify key features.
In Target B, we learned that there are three different forms of quadratic functions in which you can graph from. Those three forms are: standard form, intercept/factored form, and vertex form. Each of these forms can provide you with key features of the graph of a quadratic function. When a function is written in standard form, the y-intercept can be easily identified by looking at the “c” in the equation. When a function is written in intercept/factored form, the x-intercepts can easily identifiable, hence the name of the form: intercept form. And finally, when a function is written in vertex form, the vertex can easily be identified. This is why it is called vertex form! Look at the functions below and determine which form each function is written in, and the key feature that can be identified.


 * Function A: f(x) = (x – 5)(x + 2)**
 * Function B: f(x) = 2(x – 3) 2 + 4**
 * Function C: f(x) =** **x 2 + 3x + 10**


 * Function A** is written in intercept/factored form, therefore the x-intercepts can be found. The intercepts are (5, 0) and (-2, 0). **Function B** is written in vertex form, which means the key feature for this function would be the vertex (3, 4). **Function C** is written in standard form, and the y-intercept can be found by looking at the “c” value: (0, 10).

Now that we know the key features that can be found from each of the three different forms, let’s take a look at how to convert between each of the three forms. Why would this be beneficial to know? Let’s say you have a function written in standard form, for example, f(x) = x 2 – 6x + 8. We know that the y-intercept of the graph of this function is located at (0, 8) because the key feature for a function written in standard form is the y-intercept. But what if you were asked for the vertex of f(x) = x 2 – 6x + 8? You would need to rewrite the function in vertex form! In order to write equivalent quadratic function, use the guidelines below: To convert from:
 * **FACTORED** form to **STANDARD** form: Distribute (Click here to review how to distribute)
 * **STANDARD** form to **FACTORED** form: Factor (Click here to review how to factor)
 * **STANDARD** form to **VERTEX** form: Complete the Square (Click here to review how to complete the square)
 * **VERTEX** form to **STANDARD** form: Expand & Combine Like Terms




 * Graphing Quadratic Functions-Target D-Converting Forms of a Quad-Quick Check**

Identify the form that each function is in, and the key feature that can be found from that function. 1) **f(x) = -3(x – 7)(x – 1)** 2) **g(x) = (x + 6) 2 – 2**

Determine which form is needed. Then, write the equivalent function to find the key feature. 3) Find the vertex of **k(x) = (x + 4)(x + 2)**. 4) Find the x-intercepts of **h(x) = 2x 2 – 10x – 12**.

Graphing Quadratic Functions-Target D-Converting Forms of a Quad-Quick Check Solutions