Do Now 3/20/19 Take out HW from last night. Text p. 436, #4-26 evens, 29 Copy HW in your planner. Practice worksheet 8.3 Quiz sections 8.1-8.3 Friday, 3/22 In your notebook, answer the following. The function y = -16t2 + 64 represents the height y (in feet) of egg being dropped t seconds from a building. a. After how many seconds does egg hit the ground? b. A second egg is dropped from a height of 100 feet. Which egg hits the ground in the least amount of time? What is the difference in time of the faster egg? Explain.

Second drop: t = 2.5 seconds. Difference is 0.5 seconds.

Homework Text p. 436, #4-26 evens, 29

Homework Text p. 436, #4-26 evens, 29

Homework Text p. 436, #4-26 evens, 29

Learning Goal Learning Target SWBAT graph quadratic functions SWBAT practice graphing functions of the form f(x) = ax² + bx + c

Section 8.3 “Graph f(x) = ax² + bx + c” Properties of the Graph of a Quadratic Function y = ax² + bx + c is a parabola that: -opens up if a > 0 -opens down if a < 0 -is narrower than y = x² if the |a| > 1 -is wider than y = x² if the |a| < 1 -has an axis of symmetry @ x = -(b/2a) -has a vertex with an x-coordinate of -(b/2a) -has a y-intercept of c. So the point (0,c) is on the parabola

Finding the Axis of Symmetry and the Vertex of a Parabola Consider the graph y = -2x² + 12x – 7 (a) Find the axis of symmetry of the graph (b) Find the vertex of the graph Axis of symmetry: Substitute a = -2 b = 12 Substitute the x-value into the original equation and solve for y. The vertex of the parabola is the point (3,11)

Graph y = 3x² - 6x + 2 Step 1: Determine if parabola opens up or down Step 2: Find and draw the axis of symmetry Step 3: Find and plot the vertex Step 4: Plot two points. Choose two x-values less than the x-coordinate of the vertex. Then find the corresponding y-values. x y 2 -1 11 Step 5: Reflect the points plotted over the axis of symmetry. Step 6: Draw a parabola through the plotted points. Minimum Value

Graph y = -1/4x² - x + 1 Step 1: Determine if parabola opens up or down DOWN Step 2: Find and draw the axis of symmetry Step 3: Find and plot the vertex Step 4: Plot two points. Choose two x-values more than the x-coordinate of the vertex. Then find the corresponding y-values. x y 1 2 -2 Step 5: Reflect the points plotted over the axis of symmetry. Maximum Value Step 6: Draw a parabola through the plotted points.

Minimum and Maximum Values For y = ax² + bx + c, the y-coordinate of the vertex is the MINIMUM VALUE of the function if a > 0 or the MAXIMUM VALUE of the function if a < 0. y = ax² + bx + c; a > 0 y = -ax² + bx + c; a < 0 maximum minimum

Real-Life

A group of friends is launching water balloons A group of friends is launching water balloons. The function f(t) = -16t2 + 80t + 5 represents the height (in feet) of the first balloon t seconds after it is launched. The height of the second balloon t seconds after it is launched is shown in the graph. Which water balloon went higher?

A group of friends is launching water balloons A group of friends is launching water balloons. The function f(t) = -16t2 + 80t + 5 represents the height (in feet) of the first balloon t seconds after it is launched. The height of the second balloon t seconds after it is launched is shown in the graph. Which water balloon went higher?

EARN A BADGE!!

Homework/Classwork Practice worksheet 8.3