Sketching a Quadratic GraphStudents 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?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

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

𝑃𝑎𝑔𝑒156𝐸𝑥𝑒𝑟𝑐𝑖𝑠𝑒 4𝐿

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)

Consider the function

ii. The equation of the axis of symmetry

• General Form

• So, a = 1, b = 6, c = 8

• Use .

𝑥=−62 (1 )

=−3

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)

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)

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)

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 4LPage 158 – Exercise 4M