how do i graph quadratic functions in vertex and intercept form? how do i rewrite a quadratic in...
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• How do I graph quadratic functions in vertex and intercept form?
• How do I rewrite a quadratic in standard form?
Example 1 Graph a quadratic function in vertex formGraph a quadratic function in vertex form
GraphGraph .212
1 2 xy
3.2 Graph Quad in Vertex/Intercept Form
Solution1. Identify the constants a =
____, h = ___,
and k = ____. Because a > 0, the parabola opens ____.
12
up
2
1
2. Plot the vertex (h, k) = (___, ___) and draw the axis of symmetry at x = ____.
1 21
3. Use the pattern for the parabola to plot the other points.
a = ____
, so the graph is going up half as fast as normal.2
1
4. Draw a parabola through the plotted points.
3.2 Graph Quad in Vertex/Intercept FormCheckpoint. Graph the function. Label the vertex and Checkpoint. Graph the function. Label the vertex and axis of symmetry. axis of symmetry.
43 1. 2 xy
V ,3 4:sym of axis
3xnormal anddown
Example 2 Graph a quadratic function in intercept formGraph a quadratic function in intercept form
GraphGraph .512 xxy
3.2 Graph Quad in Vertex/Intercept Form
Solution1. Identify the x-intercepts. Because p = ____
and q = ____, the x-intercepts occur at the points (___, 0) and (___, 0).
15
12. Find the coordinates of the vertex.
5
4. Draw a parabola through the vertex and the points where the
x-intercepts occur.
____2
2
qpx 51
3
_________________ y 53132 8So, the vertex is (___, ___).3 8
3.2 Graph Quad in Vertex/Intercept FormCheckpoint. Graph the function. Label the vertex, axis Checkpoint. Graph the function. Label the vertex, axis of symmetry, and of symmetry, and xx-intercepts. -intercepts.
24 2. xxy
V ,1 9 , :int-x 0 ,4 0 ,2 2
2
2
x 24
1
2141 y 9
1x :sym of axis
3.2 Graph Quad in Vertex/Intercept FormCheckpoint. Graph the function. Label the vertex, axis Checkpoint. Graph the function. Label the vertex, axis of symmetry, and of symmetry, and xx-intercepts. -intercepts.
31 3. xxy
V ,1 4
, :int-x 0 ,1 0 ,3
1
1
2
x 31
1
3111 y 4
1x :sym of axis
Example 3 Use a quadratic model in vertex formUse a quadratic model in vertex form
10
3400
1400 2
x
y
3.2 Graph Quad in Vertex/Intercept Form
Towers Two generator towers are designed with an electric cable that connects them. The ends of the cable are the same height above the ground. The cable can be modeled by
where x is the horizontal distance (in feet) from the left tower and y is the corresponding height (in feet) of the cable. Find the distance between the towers.SolutionThe vertex of the parabola is (_____, ___). The cable’s lowest point is _____ feet from either tower. The distance between the towers is d = ___(______) = ______ feet.
1400 101400
2 1400 2800
3.2 Graph Quad in Vertex/Intercept FormCheckpoint. Complete the following exercise. Checkpoint. Complete the following exercise.
4. Suppose in Example 3, the cable is modeled by
20
2400
1500 2
x
y
Find the distance between the towers.
V ,1500 20
15002dfeet 3000
Example 4 Change quadratic function to standard formChange quadratic function to standard form
523 a. xxy
3.2 Graph Quad in Vertex/Intercept Form
825 b. 2 xy
Original function.Original function.Solution
523 a. xxyMultiply using FOIL.Multiply using FOIL._____________3 2x x5 x2 10
Combine like terms.Combine like terms._________3 2x x3 10Distributive property.Distributive property._________ 23x x9 30
Example 4 Change quadratic function to standard formChange quadratic function to standard form
523 a. xxy
3.2 Graph Quad in Vertex/Intercept Form
825 b. 2 xy
Original function.Original function.Solution
825 b. 2 xy
Rewrite (Rewrite (xx + 2) + 2)22.. 8________5 2x
Combine like terms.Combine like terms. 8________5 2x x4 4Distributive property.Distributive property.8____________ 25x x20 20
8___________5 2x x2 x2 4
2x
Multiply using FOIL.Multiply using FOIL.
Combine like terms.Combine like terms.____________ 25x x20 12
3.2 Graph Quad in Vertex/Intercept FormCheckpoint. Write the quadratic function in standard Checkpoint. Write the quadratic function in standard form. form.
1034 5. 2 xy
10334 xx 10 4 2x x3 x3 9 10 4 2x x6 9
24x x24 1036 24x x24 26
3.2 Graph Quad in Vertex/Intercept FormCheckpoint. Write the quadratic function in standard Checkpoint. Write the quadratic function in standard form. form.
673 6. xxy 3 2x x6 x7 42
3 2x x 4223x x3 126
3.2 Graph Quad in Vertex/Intercept Form
Pg. 67, 3.2 #1-29