Download presentation

Presentation is loading. Please wait.

Published byKelly Marlowe Modified over 6 years ago

2
Quadratic Equation – Equation in the form y=ax 2 + bx + c. Parabola – The general shape of a quadratic equation. It is in the form of a “U” which may open upward or downward. Vertex – The maximum or minimum point of a parabola. Maximum – The highest point (vertex) of a parabola when it opens downward. Minimum – The lowest point (vertex) of a parabola when it opens upward. Axis of symmetry – The line passing through the vertex having the equation about which the parabola is symmetric.

3
How does the sign of the coefficient of x 2 affect the graph of a parabola? On your graphing calculator, do the following: 1. Press the Y= key. 2. Clear any existing equations by placing the cursor immediately after the = and pressing CLEAR. 3. Enter 2x 2 after the Y 1 = by doing the following keystrokes. 2 X,T, x 2 4. Press GRAPH.

4
Repeat using the equation y = -2x 2. When the coefficient of x 2 is positive, the graph opens upward. When the coefficient of x 2 is negative, the graph opens downward.

5
How does the value of a in the equation ax 2 + bx + c affect the graph of the parabola? Clear the equations in the Y= screen of your calculator. Enter the equation x 2 for Y 1. Enter the equation 3 x 2 for Y 2. Choose a different type of line for Y 2 so that you can tell the difference between them. Press GRAPH.

6
Clear the second equation in the Y= screen and now enter the equation y = (1/4)x 2. Press the GRAPH key and compare the two graphs.

7
Summary for ax 2 When a is positive, the parabola opens upward. When a is negative, the parabola opens downward. When a is larger than 1, the graph will be narrower than the graph of x2.x2. When a is less than 1, the graph will be wider (broader) than the graph of x2.x2.

8
How does the value of c affect the graph of a parabola when the equation is in the form ax 2 + c? o In the Y= screen of the graphing calculator, enter x 2 for Y 1. o Enter x 2 + 3 for Y 2. o Press the GRAPH key.

9
Now predict what the graph of y = x 2 – 5 will look like. Enter x 2 for Y 1 in the Y= screen. Enter x 2 – 5 for Y 2 Press GRAPH.

10
What happens to the graph of a parabola when the equation is in the form (x-h) 2 or (x+h) 2 ? Enter x 2 for Y 1 in the Y= screen. Enter (x-3) 2 for Y 2. Press GRAPH.

11
Clear the equation for Y 2. Enter (x+4) 2 for Y 2. Press GRAPH.

12
The vertex of the graph of ax 2 will be at the origin. The vertex of the graph of the parabola having the equation ax 2 + c will move up on the y-axis by the amount c if c>0. The vertex of the graph of the parabola having the equation ax 2 + c will move down on the y-axis by the absolute value of c if c<0. The vertex of the graph of the parabola in the form (x-h) 2 will shift to the right by h units on the x-axis. The vertex of the graph of the parabola in the form (x+h) 2 will shift to the left by h units on the x-axis.

13
Compare the graphs of the following quadratic equations to each other. Check your work with your graphing calculator. 1) x 2, x 2 – 7, (x +2) 2 2) 2x 2, x 2 + 6, (1/3)(x-5) 2

14
Problem 1 All three graphs have the same shape. The vertex of the graph of x 2 – 7 will move down 7 on the y-axis. the vertex of the graph of (x+2) 2 will move left two on the x-axis.

15
Problem 2 The graph of 2x 2 will be the narrowest. The graph of (1/3)(x-2) 2 will be the broadest. The vertex of x 2 + 6 will be shifted up 6 units on the y- axis compared to the graph of 2x 2. The vertex of (1/3)(x-2) 2 will be shifted right two units on the x-axis compared to the graph of 2x 2.

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google