Standard form By: Prachi

Learning goals

  • I will learn about how to find the x-intercepts using the quadratic formula

  • I will be able to find the maximum or minimum value by completing the square

  • I will learn how to turn a standard from equation into vertex form

Summary of unit

  • The value of a gives you the shape and direction of opening (if parabola opens up or down)
  • The value of c is the y-intercept ( where parabola crosses y- axis)
  • You can solve for x- intercepts of a quadratic equation which is in standard form by using the quadratic formula
  • When solving for the x-intercepts using the quadratic equation, the value of -b changes depending on the value of b in the standard form equation. for example, if the b value in a equation is 3, you would put -3 for the -b value but if the b value in the equation is negative such as -3, you would put 3 as the -b value when solving using the quadratic formula
  • The number inside the square root in the quadratic equation is called the discriminant
  • If the discriminant is greater than 0, the equation will have 2 x-intercepts
  • If the discriminant is equal to 0, the equation will have 1 x-intercept
  • If the discriminant is less than 0, the equation will have no x-intercepts
  • You can find the maximum or minimum point of a parabola (vertex) by completing the square and turning the standard form equation into vertex form
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Quadratic formula example

  • When using the quadratic formula, you have to substitute the values of a, b and c from the original equation into the quadratic formula
  • you must make the standard form equation= 0 to solve for the x-intercept(s)
  • In equation below, the value of a is 5, the value of b is -7 and the value of c is 2
  • Something to remember: the value of the discriminant of the equation in the bottom is 9 (49-40)
  • 9 is greater than 0 so you know right away that this equation has 2 x-intercepts
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Using the Quadratic Formula

Completing the square example

  • when completing the square, you have to make a perfect square trinomial with the first two terms of the standard equation in order to make a standard form equation into vertex form
  • you also have to remember to take the common number out of the brackets if both numbers are divisible by the same number
  • you then have to divide middle term by 2 (b from bx) and square that answer to get the last term of the perfect square
  • you must remember to also minus the same number (+c-c) and multiply it with the a value and take it outside of the bracket
  • To write the final equation in vertex form for the (x-h) part, the h value is the number you divided the middle term by
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Word problem using completing the square

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