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How Do You Graph a Quadratic Equation in Intercept Form?

Graph y = 2(x + 3)(x – 1).

Summary

  1. y=2(x+3)(x-1) is in intercept form
  2. p and q are the x-intercepts of the parabola
  3. The x-intercepts are where the graph crosses the x-axis
  4. Intercept form has built-in minus signs in front of 'p' and 'q', so switch the signs of the numbers when you pick them out
  5. The axis of symmetry is the imaginary vertical line that cuts the parabola in half
  6. Since the vertex always lies on the axis of symmetry, it has the same x-value as the axis of symmetry
  7. To find the y-value for the vertex, plug -1 into the original equation and solve for y

Notes

    1. y=2(x+3)(x-1) is in a specific quadratic form, but what form is it in?
    1. 'a', 'b', and 'c' are constants in standard form
    2. 'a' cannot be zero
    3. 'a', 'h' and 'k' are constants in vertex form
    4. (h,k) is the vertex of the quadratic equation in vertex form
    5. 'a', 'p', and 'q' are constants in the intercept form
    6. In intercept form, 'p' and 'q' are the x-intercepts, or zeros, of the quadratic
    7. y=2(x+3)(x-1) is in intercept form
    1. The x-intercepts, or zeros, of the quadratic are where the graph crosses the x-axis
    1. The x-intercepts, or zeros, of the quadratic are where the graph crosses the x-axis
    2. General form for intercept form is y=a(x-p)(x-q)
    3. Our equation, y=2(x+3)(x-1), is in intercept form
    1. Since intercept form has built-in minus signs, let's think of the equation as y = 2(x-(-3))(x-1)
    2. Then it's easier to pick out p and q, the x-intercepts: p = -3 and q = 1
    3. It doesn't really matter which you call p and which you call q -- both will be x-intercepts of the graph
    1. The axis of symmetry is the imaginary vertical line that cuts the parabola in half
    2. The vertex always lies on the axis of symmetry, so finding the axis of symmetry will help us find the vertex
    1. Notice how this formula is just the average of the x-intercepts
    2. This will give us the point right in the middle of the x-intercepts
    3. This makes sense, because the axis of symmetry splits the parabola in half
    4. In our equation, p = -3 and q = 1
    5. So we add -3 and 1 to get -2, then divide by 2 to get x = -1
    6. x = -1 is the graph of a vertical line -- the vertical line that cuts the parabola in half, or the axis of symmetry!
    1. Since the vertex lies on the axis of symmetry they have the same x-value, which we just found to be -1
    1. We know that the vertex is on our parabola and that its x-value is -1
    2. So in order to find its y-value, we need to plug the x-value into the original equation and see what we get for y
    3. The equation we end up with is y = 2(-1+3)(-1-1)
    4. This becomes y = 2(2)(-2), which simplifies to y = -8
    5. So our vertex is the point (-1,-8)
    1. Since this is a quadratic equation, the graph is a parabola
    1. Since this is a quadratic equation, the graph is a parabola