1. Category 4
STAAR Tutorials – 2017

2. Day 9

3. Quadratic Functions

4. Domain & Range of Quadratics

5. Form of Quadratic Equations

6. Vertex Form of a Quadratic
h is the opposite of the x value in the vertex
k is the y value in the vertex

7. Writing Quadratic Equations Given the Vertex and a Point

8. Convert from Vertex Form to Standard Form
Expand (x – 1)2
multiply using Box or FOIL
Multiply by 3 using distributive property
Combine like terms and put in standard form

9. Quadratic Transformations
The basic function y = ax² + c has two basic transformations.
Changes to a make the graph wider or narrower
Changes to sign of ‘a’ make the graph open up or down.
Changes to c make the graph shift vertically (up or down)

10. Quadratic Transformations
In the quadratic parent function a = 1
y = x² or y = 1x²
Decreasing a to a fraction less than 1, (but still positive) makes the graph wider.

11. Quadratic Transformations, cont…
Increasing a to a number greater than 1 makes the graph narrower.
If a is a negative number, the graph opens down

12. Quadratic Transformations, cont…
Effects on c
Increasing c shifts the graph up
Decreasing c shifts the graph down

13. Day 10

14. Solving Quadratic Equations
The solutions, roots, x-intercepts or zeros of a quadratic equation are the points where the parabola crosses the x-axis

15. Solving Quadratic Equations by Graphing
You can solve a quadratic equation by graphing
To solve by graphing, the equation must be in
y = ax² + bx + c form.
Then just graph it in the calculator and see where the parabola crosses the x-axis
Or look at the table to find the points that have y = 0 (usually 2 but could be one or none and may not always show up in the table)

16. Solving Quadratic Equations by Graphing
Example: What are the roots of the quadratic equation x² - x – 6 = 0?
x = -2
x = 3

17. Solving Quadratics Using the calculator
Example: The area of a rectangle is 3x² + 19x – 14, and the width is x Which expression best describes the rectangle’s length?
A. (2x – 3) B. (3x – 2) C. (2x – 7) D. (3x – 7)
A = length ▪ width
3x² + 19x – 14 = length ▪ (x + 7)

18. Solving Quadratics Using the Quadratic Formula

19. Solve Quadratics by Factoring

20. Solving by Completing the Square

22. Solving by Taking Square Roots
If your Quadratic equation has no ‘x’ (only ‘x2 ’), you can solve by taking the square root.
Ex. x2 = 9
x2 +3 = 19
4x = 12

23. Interpreting Quadratic Graphs
Pay attention to the labels on the x- and y- axes
Read the question carefully
Example: How much time elapses while the rocket is 600 feet above the ground?
4 seconds
5, A.09D

24. Parent Functions y = abx y = x y = x² (Y = 1x + 0) (Y = 1x2 + 0x + 0)
There are three parent functions on the STAAR test:
Linear
Exponential
Quadratic
y = x
(Y = 1x + 0)
y = x²
(Y = 1x2 + 0x + 0)
y = abx
M = 1 1
B = 0
Opens up
Vertex at (0, 0)
y axis is axis of symmetry