Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
2. Characteristics of Quadratic Functions
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Exercise 7 Page 59

Identify the x-intercepts first. Then use it to find the axis of symmetry.

x-intercepts: x=2 and x=6
Axis of Symmetry: x=4
Vertex: (4,- 1)
Graph:

Practice makes perfect

To graph the quadratic function given in intercept form f(x)=a(x-p)(x-q), we must start by identify the values of a, p, and q. g(x)=1/4(x-6)(x-2) ⇕ g(x)=1/4(x-6)(x-2) We can see that a=14, p=6, and q=2. Now, we will follow four steps to graph the function.

  1. Identify the x -intercepts.
  2. Plot the x-intercepts and find the axis of symmetry.
  3. Calculate the vertex and plot it.
  4. Connect the points with a parabola.

    Identifying the x -intercepts

    Recall that the x-intercepts of a function written in intercept form are the values of p and q. Thus, the points where our function intercepts the x-axis are (6,0) and (2,0).

    Finding the Axis of Symmetry

    The axis of symmetry is halfway between the x-intercepts, (p,0) and (q,0). Therefore, it has the following equation. x= p+q2 Since we already know the values of p and q, we can substitute them into the formula.
    x=p+q/2
    x=6+(2)/2
    â–Ľ
    Simplify right-hand side
    x=8/2
    x=4
    The axis of symmetry of the parabola is the vertical line with equation x=4. Let's plot the x-intercepts and the axis of symmetry on a coordinate plane.

    Calculating the Vertex

    The x-coordinate of the vertex is the same as the formula for the axis of symmetry, x= 4. To find the y-coordinate, we need to substitute 4 for x in the given equation.
    g(x)=1/4(x-6)(x-2)
    g( 4)=1/4( 4-6)( 4-2)
    â–Ľ
    Simplify right-hand side
    g(4)=1/4(- 2)(2)
    g(4)= - 1
    We found the y-coordinate, and now we know that the vertex is (4,- 1). Let's plot it on our coordinate plane.

    Connecting the Points

    We can now draw the graph of the function. Since a=14, which is positive, the parabola will open upwards. Let's connect the three points with a smooth curve.