Section 2.6 Quadratic Functions. y = x 2 How many real zeros does it have? How many real zeros can a quadratic function have?

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Presentation transcript:

Section 2.6 Quadratic Functions

y = x 2 How many real zeros does it have? How many real zeros can a quadratic function have?

y = x 2 +1 No real zeros!

y = 3x 2 +5x-2 This function has two real zeros Let’s find the zeros

Quadratic Formula Use the quadratic formula to find the zeros of y = 3x 2 +5x-2 Use the quadratic formula to find the zeros of y = x 2 +1

A ball thrown upward from a bridge that falls all the way to the ground (past the bridge) has a height, h, that can be modeled as a function of time, t by –How high is the bridge? –When does the ball hit the ground? –Sketch the graph Use a window that shows the height of the ball from when it is thrown until it hits the ground

Let d(t) = 16t 2 be the distance, in feet, that an object has fallen after t seconds. Compute the average speed of the object over each of the following time intervals –0 ≤ t ≤ 1 –1 ≤ t ≤ 2 –2 ≤ t ≤ 3 –3 ≤ t ≤ 4 What is happening with the average speeds? Is the graph concave up or concave down?

In your groups work on problems 6, 14, and 15