Download The Graph of a Quadratic Function


Graph the following transformations
f ( x)  ( x  2)  3 f ( x)  2( x  1)  4
2
Warm - Up
2

Assignment
◦ p. 214
◦ #12, 13, 16, 17, 20, 22, 24,
Cargo Pants Legends
 Make Up Tests

◦ After School Today and Tomorrow

Test Corrections
◦ After School Wednesday and Thursday
Announcements
2.1 Quadratic Functions
Section Objectives: Students will know how to sketch
and analyze graphs of quadratic functions.
Quadratic functions

f(x) = ax2 + bx + c, with a  0.
 The graph of a quadratic function is a
parabola.
 y = x2

◦ Vertex?

y = -x2
◦ Vertex?
The Graph of a Quadratic Function

The quadratic function standard form
f(x) = a(x – h)2 + k, a  0
Vertex at (h, k).
 If a > 0, the parabola opens _______
 If a < 0, the parabola opens _______

The Standard Form of a Quadratic
Function
Is it a perfect square??

Yes
◦ Factor/Use Quadratic
Formula to find the
vertex.
x  2x 1
2
•No
•Complete the Square
to find the vertex
x  3x  4
Changing a trinomial
into vertex form
2
ax  bx  c
2
The vertex is at
2
(2, -6), the parabola
f ( x)  x  4 x  2
opens upward, and
2
f ( x)  x  4 x  2
there is no change in
2
 x  4 x  4  4  2 the width.



 x  2  6
2
Warm Up - Graph the following
quadratic function.

Assignment
◦ p. 214
◦ # 32, 34, 37, 38, 39, 44, 70

Make Up Tests
◦ After School Today

Test Corrections
◦ After School Tomorrow and Thursday
Announcements
p. 214
 #12, 13, 16, 17, 20, 22, 24,

Assignment Questions?
f ( x)  x  8x  16
2
f ( x)  x 2  8 x  16
 x  4x  4
 x  4
2
Vertex: (4, 0)
Find the vertex of the following
parabola.
•To find the x – intercept: •To find the y – intercept:
•Set “y” equal to 0
•Set “x” equal to 0
•Solve for x
•Solve for y
y   x  5  6
2
y   x  5  6
2
0   x  5  6
2
6   x  5
5 6  x
y  0  5  6
2
y  5  6
2
2
 6  x5
y   x  5  6
2
y  25  6
(5  6, 0)
y  19
(0,19)
Find the x and y intercepts

y = (x – 4)2 + 5.
◦ What is the minimum value of y?
Finding Minimum and Maximum
Values of Quadratics
From the vertex we have this much of the
equation: f(x) = a(x – 1)2 – 2.
 To find a we substitute the point (3, 6)
and solve for
a.
2

6  a3  1  2
6  4a  2
8  4a
2a
The equation is f(x) = 2(x – 1)2 – 2.
Example 3. Find the standard form of
the equation of the parabola that has
vertex (1, -2) and passes through the
point (3, 6).

Example 4. The daily cost of manufacturing a particular
product is given by C(x) = 1200 – 7x + 0.1x2
where x is the number of units produced each day.
Determine how many units should be produced daily to
minimize cost.
 Algebraic Solution
Graphical Solution
 We need to find h.

C ( x)  1200  7 x  0.1x 2
 0.1 x 2  70 x  1200
 0.1 x 2  70 x  352  1200  122.5
2
 0.1x  35  1322.5





Producing 35 units per day will minimize cost.
Mo’ Money, Long Problems