www.VirtualNerd.com

How Do You Graph the Parent Quadratic Function y=x2?

Graph y = x2.

Summary

  1. y = x2 is a quadratic function, which means its graph is a parabola
  2. Quadratic functions have the form y = ax2 + bx + c
  3. Since there is no coefficient in front of the x2, that means we have an invisible 1
  4. So our value for 'a' is 1
  5. Since we don't have an 'x' term or a constant, our values for 'b' and 'c' are 0
  6. The axis of symmetry is at x = 0, which is the y-axis
  7. The vertex is (0,0), which is the origin

Notes

    1. The axis of symmetry is the vertical line that cuts the parabola into two symmetrical halves
    1. The graph of a quadratic function is a parabola
    1. The axis of symmetry is the vertical line that cuts the parabola into two symmetrical halves
    2. Quadratic functions have the form y = ax2 + bx + c
    3. In the quadratic y = x2, a = 1 and b = 0
    4. So the axis of symmetry is at x = 0, which is the y-axis
    1. The vertex is where a quadratic function intersects the axis of symmetry
    1. The axis of symmetry is the vertical line that cuts the parabola into two symmetrical halves
    2. The axis of symmetry is at x = 0
    1. Since the vertex is on the axis of symmetry, which is the line x = 0, it has the same x-value
    2. The vertex is also on the parabola, so we can plug that x-value into our function to find the y-value for the vertex
    1. When we plug 0 in for 'x' into y = x2, we get y = 02, which is just 0
    2. So that means our y-value is 0 as well!
    1. Use a table to find points that are on the graph of y = x2
    1. The vertex is at the origin: the point (0,0)
    2. We want to choose some values for 'x' on either side of the vertex, so we can see what's happening on both sides of the parabola
    3. We're going to choose -2, -1, 0, 1, and 2 as the x-values
    4. Then we'll plug those values into y = x2 to find their corresponding y-values
    1. We're choosing -2, -1, 0, 1, and 2 as the x-values
    2. Remember, the vertex is at the point (0,0), where x = 0
    3. Make sure to put parentheses around the negative numbers when you square them, so that you square the negative too!
    4. Simplify each square to find the values for 'y'
    5. Put the x's and y's together to make ordered pairs we can use to graph the parabola!
    1. The ordered pairs were:
    2. (-2,4), (-1,1), (0,0), (1,1), and (2,4)
    1. The parent function is the simplest form of a particular type of function
    2. In order to be a quadratic, a function needs to have an x2 term
    3. That's all the function y = x2 has -- you can't get any simpler than that and still be a quadratic!
    4. So y = x2 is the parent quadratic function