Download presentation

Published byBarnard Greer Modified over 5 years ago

1
**Graphing Quadratic Equations in Vertex and Intercept Form**

Section 4.2 Graphing Quadratic Equations in Vertex and Intercept Form

2
**The y intercept of the graph is c if the equation is in STANDARD FORM **

Quadratic Functions A quadratic function has the form: f (x) = ax2 + bx + c Where a, b and c are real numbers and a is not equal to 0. The y intercept of the graph is c if the equation is in STANDARD FORM . The basic shape of the graph is a PARABOLA or U shaped

3
Positive Quadratic Negative Quadratic y = ax2 y = -ax2 Parabolas always have a lowest point (minimum) or a highest point (maximum, if the parabola is upside-down). This point, where the parabola changes direction, is called the "vertex".

4
**Vertex- Axis of symmetry- The lowest or highest point of a parabola.**

The vertical line through the vertex of the parabola. Axis of Symmetry

5
**Vertex Form: y = a(x – h)2 + k, - the vertex is the point (h, k). **

- the axis of symmetry is x = h - if “a” is positive it opens up - if “a” is negative it opens down Plot the vertex and then find two other points by using “a” as your rise/run

7
**Vertex Form (x – h)2 + k – vertex form**

Each function we just looked at can be written in the form (x – h)2 + k, where (h , k) is the vertex of the parabola, and x = h is its axis of symmetry. (x – h)2 + k – vertex form Equation Vertex Axis of Symmetry y = x2 or y = (x – 0)2 + 0 (0 , 0) x = 0 y = x2 + 2 or y = (x – 0)2 + 2 (0 , 2) y = (x – 3)2 or y = (x – 3)2 + 0 (3 , 0) x = 3

8
**(-2, 5) EXAMPLE A Graph a quadratic function in vertex form 12**

Graph y = – (x + 2)2 + 5. SOLUTION STEP 1: Identify the vertex (-2, 5) STEP 2: Plot the vertex & draw the line of symmetry STEP 3: Determine if it opens up or down

9
EXAMPLE A Graph a quadratic function in vertex form 12 Graph y = – (x + 2)2 + 5. STEP 4: Use “a” as your rise/run Down 1 and over 2 STEP 5: Draw a parabola

12
**Example B: Graph y = (x + 2)2 + 1**

Analyze y = (x + 2)2 + 1. Step 1 Plot the vertex (-2 , 1) Step 2 Draw the axis of symmetry, x = -2. Step 3 Find and plot two points on one side , such as (-1, 2) and (0 , 5). Step 4 Use symmetry to complete the graph, or find two points on the left side of the vertex.

13
**Example C: Graph y=-.5(x+3)2+4**

a is negative (a = -.5), so parabola opens down. Vertex is (h,k) or (-3,4) Axis of symmetry is the vertical line x = -3 Table of values x y -1 2 -3 4 -5 2 Vertex (-3,4) (-4,3.5) (-2,3.5) (-5,2) (-1,2) x=-3

14
Now you try one!

15
**Minimum “a” is positive Maximum “a” is negative**

GUIDED PRACTICE for Examples 1 and 2 Graph the function. Label the vertex and axis of symmetry. y = (x + 2)2 – 3 Minimum “a” is positive y = –(x + 1)2 + 5 Maximum “a” is negative

20
**Intercept Form Equation**

y=a(x-p)(x-q) The x-intercepts are the points (p,0) and (q,0). The axis of symmetry is the vertical line x= The x-coordinate of the vertex is To find the y-coordinate of the vertex, plug the x-coord. into the equation and solve for y. If “a” is positive, parabola opens up If “a” is negative, parabola opens down.

22
**Example D: Graph y=-(x+2)(x-4)**

Since a is negative, parabola opens down. The x-intercepts are (-2,0) and (4,0) To find the x-coord. of the vertex, use To find the y-coord., plug 1 in for x. Vertex (1,9) The axis of symmetry is the vertical line x=1 (from the x-coord. of the vertex) (1,9) (-2,0) (4,0) x=1

27
**Now you try one! y=2(x-3)(x+1) Open up or down? X-intercepts? Vertex?**

Axis of symmetry?

28
x=1 (-1,0) (3,0) (1,-8)

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