Warm - Up Graph the following transformations. Announcements Assignment ◦p. 214 ◦#12, 13, 16, 17, 20, 22, 24, Cargo Pants Legends Make Up Tests ◦After.

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Presentation transcript:

Warm - Up Graph the following transformations

Announcements 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

2.1 Quadratic Functions Section Objectives: Students will know how to sketch and analyze graphs of quadratic functions.

The Graph of a Quadratic Function Quadratic functions f(x) = ax 2 + bx + c, with a  0. The graph of a quadratic function is a parabola. y = x 2 ◦Vertex? y = -x 2 ◦Vertex?

The Standard Form 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 _______

Changing a trinomial into vertex form Yes ◦Factor/Use Quadratic Formula to find the vertex. Is it a perfect square?? No Complete the Square to find the vertex

Warm Up - Graph the following quadratic function. The vertex is at (2, -6), the parabola opens upward, and there is no change in the width.

Announcements Assignment ◦p. 214 ◦# 32, 34, 37, 38, 39, 44, 70 Make Up Tests ◦After School Today Test Corrections ◦After School Tomorrow and Thursday

Assignment Questions? p. 214 #12, 13, 16, 17, 20, 22, 24,

Find the vertex of the following parabola. Vertex: (4, 0)

Find the x and y intercepts To find the x – intercept: Set “y” equal to 0 Solve for x To find the y – intercept: Set “x” equal to 0 Solve for y

Finding Minimum and Maximum Values of Quadratics y = (x – 4) ◦What is the minimum value of y?

Example 3. Find the standard form of the equation of the parabola that has vertex (1, -2) and passes through the point (3, 6). 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. The equation is f(x) = 2(x – 1) 2 – 2.

Example 4. The daily cost of manufacturing a particular product is given by 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. Producing 35 units per day will minimize cost. Mo’ Money, Long Problems C(x) = 1200 – 7x + 0.1x 2