2003 The Olympic Dream.

Slides:

Advertisements

Similar presentations

1.Find the vertex point, (h, k): 2.a will be the a from the standard form equation. 3. Substitute into y = a (x-h) 2 + k.

Advertisements

STRAIGHT LINE GRAPHS y = mx + c.

 Understand that the x-intercepts of a quadratic relation are the solutions to the quadratic equation  Factor a quadratic relation and find its x- intercepts,

Y – Intercept of a Line The y – intercept of a line is the point where the line intersects or “cuts through” the y – axis.

Straight line graphs Mahobe. Draw the graphs of the lines.

Quadratic Graph Drawing.

Graphing Quadratic Functions

Use intercepts to graph an equation

Introduction Imagine the path of a basketball as it leaves a player’s hand and swooshes through the net. Or, imagine the path of an Olympic diver as she.

Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – Find.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Graphs - Excellence Mahobe. Beatrice is entered in the discus throwing event. One day at training she has a warm-up throw in which her coach videos her.

SOLUTION STEP 1 Use intercepts to graph an equation EXAMPLE 2 Graph the equation x + 2y = 4. x + 2y = 4 x =  x- intercept 4 Find the intercepts. x + 2(0)

Holt McDougal Algebra Graphing Quadratic Functions Graph a quadratic function in the form y = ax 2 + bx + c. Objective.

CONFIDENTIAL 1 Graphing Quadratic Functions. CONFIDENTIAL 2 Warm Up Find the vertex of each parabola: 9) y = x 2 + 4x - 7 1) y = -5x x + 3 2) y.

An Introduction to Straight Line Graphs Drawing straight line graphs from their equations. Investigating different straight line graphs.

9-3 Graphing Quadratic Functions Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.

Solve the equation for y. SOLUTION EXAMPLE 2 Graph an equation Graph the equation –2x + y = –3. –2x + y = –3 y = 2x –3 STEP 1.

Notes Over 2.8 Graphing an Absolute Value Function xy Vertex: Axis of Symmetry: Slope: ( 1, 2 ) x = 1 up 2, right/left.

Writing equations given 2 points on the line. Write the equation of the line that goes through the points (1, 6) and (3, -4) m = y₂ - y₁ x₂ - x₁ -4 -

 Another method of writing an equation in vertex form is to complete the square  If you have an equation in the form h = -2.25x x , where.

QUADRATIC FUNCTIONS. IN THE QUADRATIC FUNCTION Y = AX 2 + BX + C…  What does the “a” tell you?  The width of the parabola  The greater the |a| the.

Warm Up x = 0 x = 1 (–2, 1) (0, 2) Find the axis of symmetry.

Graphing Function Charts. X Y I Y = 2X + 1 X Y ½ Y - intercept 0, 1 X - intercept -½, 0.

Determine the x and y intercepts. Find the card that matches.

2.1Intercepts;Symmetry;Graphing Key Equations

Writing Linear Equations

Introduction Imagine the path of a basketball as it leaves a player’s hand and swooshes through the net. Or, imagine the path of an Olympic diver as she.

5.3 a Slope-Intercept Form

Functions Unit 8.

Using The Discriminant

Standard Form I can identify intercepts from an equation.

Intercepts, Symmetry, Even/Odd and intersections

Graphs of Equations In Two Variables; Intercepts; Symmetry

Quadratic Graph Drawing.

Warm Up 1) Solve (2x + 3)(x – 4) = 0 2) Factor 16x3 – 4x2

Y – Intercept of a Line The y – intercept of a line is the point where the line intersects or “cuts through” the y – axis.

Chapter 1: Lesson 1.2 Graphs of Equations

Notes Over 1.1 To check for y-axis symmetry replace x with -x.

parabola up down vertex Graph Quadratic Equations axis of symmetry

Quad Frame Vertex Name: For each equation:

3.5 Write and Graph Equations of Lines

Writing Linear Equations When Given Two Points on the Line

Creating & Graphing Quadratic Functions Using the X-Intercepts (3.3.2)

Real World Problem Solving Quadratic Equations 8

X- and y- intercepts.

Ordered pairs: ( , ) ( , ) ( , ) Ordered pairs: ( , ) ( , ) ( , )

Graph 2x + 4y = 16 by finding the x and y intercepts.

Keeper 2 Honors Calculus

Geometry Section 3.5.

Graphing linear equations

Objectives Graph a line using slope-intercept form.

Quadratic Graph Drawing.

Section 8.3 Part 2 Slope and y-intercept pages

Graphing with X- and Y-Intercepts

Graphing Key Equations

6 minutes Warm-Up 1. Find the slope of the line containing the points (-2,5) and (4,6). 2. Find the slope of the line y = x – Find the slope of the.

11.2 Slope: y-intercept: 5.

Calculate points from this table and plot the points as you go.

Solving Quadratic Equations by Graphing 9-5

Quad Frame Vertex Name: For each equation:

Quadratic Graph Drawing.

Sometimes b or c is missing!

Warm Up Find the x-intercept of each linear function.

Presentation transcript:

2003 The Olympic Dream

1 3

Question 2

When t = 30 C = 150 + 20 = 170

Which ONE of the three phone cards has the highest connection fee per call?

Keep in touch card

How is this shown by the graphs?

Highest point on Cost axis (highest y intercept) - 40 c

How long is a call that costs the same using the No Frills card and the Keep in Touch card?

20 minutes

How is this shown by the graph?

The intersection of the two lines.

Use the graph to write the equation for the No Frills card.

Use the graph to write the equation for the Keep in Touch card.

Question 3

Write the equation for h, the height above the water, in terms of time, t, that models Wendy’s dive until she touches the bottom of the pool. The graph is upside down and moved ‘0.5’ in the x direction. It goes through the points (0, 4) and (2, 0)

Equation is using symmetry The graph is upside down and moved ‘0.5’ in the x direction. It goes through the points (0, 4) and (2, 0)

Because the y-intercept is 4, the equation is The graph is upside down and moved ‘0.5’ in the x direction. It goes through the points (0, 4) and (2, 0)

Write an equation that models her return from the bottom of the pool back to the surface. You may wish to draw on the graph above.

The line goes through the point (7, 0) so 0 = 2 x 7 + c  c = -14

(a) Wendy knows that to achieve a perfect dive, her hands must be within 4 metres of the bottom of the pool 2.5 seconds after starting her dive.

(a). First we need to know where she is at 2. 5 secs (a) First we need to know where she is at 2.5 secs. Substitute into the equation.

Next we need to know where the bottom of the pool is by finding where the two graphs meet.

The graphs meet at -8 so the pool is 8 m deep.