Graph Analysis Challenge

Name:

Date:

📊 Part 1: Coordinate Analysis

1. The graph below shows a straight line passing through points A(-2, 1) and B(4, 7).

Graph showing coordinate grid with line AB plotted

a) Calculate the gradient of line AB.

b) Find the equation of the line in the form y = mx + c.

2. The graph shows the curve y = x² - 4x + 3.

Graph showing parabola with vertex at (2, -1) and x-intercepts at (1, 0) and (3, 0)

a) State the coordinates of the vertex: ( _____ , _____ )

b) Find the y-intercept: ( _____ , _____ )

c) Solve x² - 4x + 3 = 0 using the graph.

3. The velocity-time graph below shows the motion of a cyclist over 8 seconds.

Velocity-time graph: 0-2s: constant 10 m/s, 2-5s: decreasing linearly from 10 m/s to 4 m/s, 5-8s: constant 4 m/s

a) Calculate the acceleration between t = 2s and t = 5s.

b) Find the total distance travelled by calculating the area under the curve.

4. Sketch the graph of y = 2ˣ - 1 for -2 ≤ x ≤ 3.

Grid provided for sketching exponential function

a) State the y-intercept: ____________

b) Write down the equation of the horizontal asymptote: y = ____________

c) Find the value of y when x = 2: ____________

5. The graph shows the function f(x) = sin(2x) for 0° ≤ x ≤ 360°.

Graph showing sine curve with period 180°, amplitude 1, passing through origin

a) State the period of the function: ____________

b) Write down all values of x where f(x) = 0:

c) Find the maximum value of the function and state where it first occurs:

Maximum value: ____________ at x = ____________