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How Do You Convert a Quadratic Equation from Intercept Form to Standard Form?

Write y = 2(x + 3)(x - 1) in standard form.

Summary

  1. y=2(x+3)(x-1) is in intercept form
  2. y=a(x-p)(x-q) is the general form for intercept form
  3. In intercept form, 'p' and 'q' are the x-intercepts
  4. So in our equation, the x-intercepts are -3 and 1
  5. y=ax2+bx+c is the general form for standard form
  6. 'a', 'b', 'c', 'p', and 'q' are constants
  7. Multiply the binomials together using FOIL
  8. Distribute the 2 into the parentheses
  9. y=2x2+4x-6 is standard form of the equation y=2(x+3)(x-1)

Notes

    1. y=a(x-p)(x-q) is the general form for intercept form
    2. In intercept form, 'p' and 'q' are the x-intercepts
    3. Right now our equation, y=2(x+3)(x-1), is in intercept form
    4. We want to get put it into standard form, which is the form y=ax2+bx+c
    5. 'a', 'b', 'c', 'p', and 'q' are all constants
    6. Notice that 'a' is the same in both standard and intercept form
    1. FOIL together the two binomials on the right, (x+3)(x-1)
    1. Make sure to keep the 2 out front as you FOIL!
    2. Multiply the First terms together, x•x=x2
    3. Multiply the Outer terms together, x•(-1)=-x
    4. Multiply the Inner terms together, 3•x=3x
    5. Multiply the Last terms together, 3•(-1)=-3
    1. Distribute in the 2 in front of x2+2x-3
    1. Distribute in the 2 in front of x2+2x-3
    2. To distribute the 2, multiply it by each term of x2+2x-3
    1. Notice that a = 2 in both standard form and intercept form!