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Sketching a Quadratic Graph

Sketching a Quadratic Graph. Students will use equation to find the axis of symmetry, the coordinates of points at which the curve intersects the x-axis, and the coordinates of the vertex. Draw the graph of note a = 1. Use your GDC to draw the graph. Where does it intersect the x-axis?

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Sketching a Quadratic Graph

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  1. Sketching a Quadratic Graph Students will use equation to find the axis of symmetry, the coordinates of points at which the curve intersects the x-axis, and the coordinates of the vertex.

  2. Draw the graph of note a = 1 Use your GDC to draw the graph. Where does it intersect the x-axis? What is the equation of its axis of symmetry? What are the coordinates of the vertex? For the general curve How can we answer the three questions above? You may want to draw more graphs in this form

  3. You may wish to draw more graphs of functions of this form.

  4. Consider the function i. Find the point where the graph intersects the y-axis • General Form • So, a = 1, b = 6, c = 8 • The curve intersects the y-axis at (0, c). (0,8)

  5. Consider the function ii. The equation of the axis of symmetry • General Form • So, a = 1, b = 6, c = 8 • Use .

  6. Consider the function iii. The coordinates of the vertex • The x-coordinate of the vertex is . So, x = – 3 • To find the y-coordinate substitute x = – 3 into the equation of the function The vertex is at (– 3, -1)

  7. Finding the x-intercepts: • The function intersects the x-axis where . • The x-values of the points of intersection are the two solutions (or roots) of the equation . • (The y-values at these points of intersection are zero)

  8. Consider the function iv. The coordinates of the point(s) of intersection with the x-axis • The curve intersects the x-axis where, so put • when x = –2 or –4. The x-intercepts are at (–2, 0) and (–4, 0)

  9. Use the information to sketch parabola • y-intercept (0, 8) • Axis of Symmetry x = –3 • Vertex (–3, –1) • x-intercepts (–2, 0) and (–4, 0) Note a > 0, so opens up • Homework: • Page 156 – Exercise 4L • Page 158 – Exercise 4M

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