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 54 Page 63

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

x-intercepts: x=- 1 and x=3
Axis of Symmetry: x=1
Vertex: (1,- 4)
Graph:

Practice makes perfect

To graph the quadratic function given in intercept form f(x)= a(x- p)(x- q), we must start by identifying the values of a, p, and q. y=(x+1)(x-3) ⇕ y= 1(x-( - 1))(x- 3) We can see that a= 1, p= - 1, and q= 3. 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 ( - 1,0) and ( 3,0).

    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=- 1+ 3/2
    â–Ľ
    Simplify right-hand side
    x=2/2
    x=1
    The axis of symmetry of the parabola is the vertical line with equation x=1. 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= 1. To find the y -coordinate, we need to substitute 1 for x in the given equation.
    y=(x+1)(x-3)
    y=( 1+1)( 1-3)
    â–Ľ
    Simplify right-hand side
    y=2(- 2)
    y= - 4
    We found the y-coordinate, and now we know that the vertex is (1,- 4). Let's plot it on our coordinate plane.

    Connecting the Points

    We can now draw the graph of the function. Since a= 1, which is positive, the parabola will open upwards. Let's connect the three points with a smooth curve.