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Lesson 4

1. Lesson 4

1.8. Explore 3

Mathematics 20-2 M3 Lesson 4

Module 3: Quadratics

 
Self-Check 3
  1. For the following graph, write the function in vertex form. Answer

    This graph shows a parabola with vertex at (6, 5) and x-intercepts at 1 and 11.

  2. A children’s wading pool that has a parabolic profile is located at a playground. The depth of the pool, in metres measured from the edge of the pool, is modelled by the function y = 0.012(x – 5)2 – 0.3.

    1. What is the axis of symmetry of the graph?

    2. What is the maximum depth of the pool?

    3. How wide is the pool?

    4. If the water level was down by 0.05 m, how wide would the top of the water be? (Make sure to round your answer to two decimal places.)

    5. Officials want to paint a stripe around the pool at a depth of 0.15 m to give parents and toddlers a visual reminder of the increasing depth. How far from the edge of the pool should the line be painted?

      Answer

textbook
  1. Complete “Practising” question 12 on page 366 of your textbook. Answer

Graphs of quadratic functions may have zero, one, or two x-intercepts. This is dependent on the location of the vertex and the direction in which the parabola opens.

This shows three graphs. In all three graphs, the parabola opens upwards. The first graph has two x-intercepts, and the vertex is below the x-axis. The second graph has one x-intercept, and the vertex is on the x-axis. The third graph has no x-intercepts, and the vertex is above the x-axis.

CREDIT: From: CANAVAN-MCGRATH ET AL. Principles of Mathematics 11, © 2012 Nelson Education Limited. p. 362. Reproduced by permission.


One way to determine the number of x-intercepts is by looking at a graph of the function. But is it possible to predict whether a quadratic function will have zero, one, or two x-intercepts if you are only given the function expressed in vertex form (i.e., not given a graph)?