Modeling Data With Quadratic Functions Section 5.2 Modeling Data With Quadratic Functions

Example 1 Graph 𝑦=− 1 2 𝑥 2 +2.

Example 2 Graph 𝑦=2 𝑥 2 −4.

Example 3 Graph 𝑦=−5+3 𝑥 2 .

Properties of a Parabola

Properties: Graph of a Quadratic Function in Standard Form

Example 4 Graph the function 𝑦= 𝑥 2 −2𝑥−3. Label the vertex and the axis of symmetry.

Example 5 Graph the function 𝑦=− 1 3 𝑥 2 −2𝑥−3. Label the vertex and the axis of symmetry.

TOTD Graph the function 𝑦=− 𝑥 2 −3𝑥+6. Label the vertex and axis of symmetry.

Example 6 Find the function’s minimum value. 𝑦=3 𝑥 2 +12𝑥+8

Example 7 Find the function’s minimum value. 𝑦=2 𝑥 2 +8𝑥−1

Example 8 Physics The equation for the motion of a projectile fired straight up at an initial velocity of 64 ft/sec is h = 64t – 16t2, where h is the height in feet and t is the time in seconds. Find the time the projectile needs to reach its highest point. How high will it go?

Example 9 A rock club’s profit from booking local bands depends on the ticket price. Using past receipts, the owner find the profit p can be modeled by the function 𝑝=−15 𝑡 2 +600𝑡+50, where t represents the ticket price in dollars. What price yields the maximum profit? What is the maximum profit? What price would you pay to see your favorite local band? How much profit would the club owner make using that ticket price?

TOTD What is the minimum value of the function y = 3x² + 2x – 8?