<meta http-equiv="refresh" content="1; url=/nojavascript/"> Graphs of Quadratic Functions ( Study Aids ) | Analysis | CK-12 Foundation

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### Vocabulary

Fill in the empty boxes.

 Word Definition ___________ The characteristic shape of a quadratic function graph, resembling a bowl or the silhouette of a bell Vertex ______________________________________________________________ Quadratic Form ______________________________________________________________ ___________ $f(x)=ax^{2}+bx+c$ Standard Form ______________________________________________________________ ___________ excellent for finding x -intercepts, is: $f(x)=a(x-r_{1})(x-r_{2})$

### Factoring Polynomials

##### Choose a name for each method to help you remember. Also, fill in any blanks.
 Method Equation Example Steps ________________________ $2x^4-x^2-15$ $ac = -30$ $& 2x^4-x^2-15\\& 2x^4-6x^2+5x^2-15\\& 2x^2(x^2-3)+5(x^2-3)\\& (x^2-3)(2x^2+5)$ ________________________ $81x^4-16$ Difference of squares: $& 81x^4-16\\& (9x^2-4)(9x^2+4)$ Factor $9x^2-4$ with difference of squares also: _______________________________ ________________________ $6x^5-51x^3-27x = 0$ Pull out Greatest Common Factor: ________________________________ Use a combination of the first two methods to factor the rest: _________________________________

Remember:
Pull out the Greatest Common Factor if there is one!

Complete the following table.

 Form Equation Used For ___________ $f(x)=ax^{2}+bx+c$ ________________________ Vertex Form ________________________ ________________________ ___________ ________________________ finding x -intercepts
1. Which letter of which form is the y-intercept? _____________________
2. Where is the vertex in vertex form_____________________
3. How do you find the vertex in standard form_____________________
4. What is the axis of symmetry and how do you find it from standard form_____________________

### Practice

##### Factor the following completely:
1. $x^4-4x^2-45$
2. $4x^4-11x^2-3$
3. $16x^4-1$
4. $6x^5+26x^3-20x$
5. $625-81x^4$
1. Which direction does a parabola open if the leading coefficient ( ) is negative?

2. Consider the quadratic functions$y = 4x^2$    $y = 5x^2$    $y = 7x^2$ Which quadratic function would you expect to have the widest parabola? Explain your answer.

##### Sketch the graph of each function:
1. $y = -x^2 + 7$
2. $y = 3x^2 + 6x +1$
3. $y = \frac{1}{2} x^2 + 2x +4$
4. $y = (x + 6)^2 - 3$
5. $y = -x^2 -8x -17$