Quadratic Relationships Website

Unit 3: Standard Form


Welcome to my website. Here you will learn everything about Standard Form Quadratics. Scroll down to see word problems and examples of Standard Form equation.

Learning Goals

  • I am able to use the quadratic formula in a quadratic equation.
  • I am able to use the standard form equation, to complete the square, and graph the parabola
  • I am able to find the x-intercepts of the equation, by using the quadratic formula.
  • I am able to find the vertex of the equation, by completing the square.
  • I am able to graph the x-intercepts and the vertex, then draw the parabola.



"a" value: represents the parabola's direction of opening and shape (stretched or compressed)

"c" value: represents the y-intercept

Quadratic Formula

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The quadratic equation is used when you are given a standard form equation and are asked to find out the x intercepts.

When asked to find out how many solutions(x-intercepts) there are you can use a simple equation to find out the number of solutions.

For Example

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The Discriminant adapts the formula that is inside the square root of the Quadratic Formula (b^2-4ac). The Discriminant helps us find out how many solutions the given quadratic equation will have, without us solving the entire equation with the Quadratic Formula. If the value of “d” is less than 0, so if it’s a negative, there will be no solutions. If the value of d is greater than 0, there will be 2 solutions and if the value of d is 0, there will be 1 solution. So to sum up the Discriminant:

  • D<0- no solutions

  • D>0- 2 solutions

  • D=0- 1 solution

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Graphing Standard Form

  1. Find the x-intercepts of the equation with the quadratic formula
  2. Find the vertex by completing the square
  3. Graph x intercepts
  4. Graph vertex
  5. Draw parabola

Completing the Square

To complete the square, divide b by two then square the quotient. Then, if a isn't 1, add and subtract that product to the standard form equation. If a were 1, add the negative value of the product. Add the negative value and c value together after multiplying it with a if a does not equal 1. Put everything with the exception of the c value in brackets and use perfect squares method to solve by factoring. Next, put the factored part and add the c value. The result will be that your successfully converted it into vertex form.

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Word Problem

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Video Using Quadratic Formula

Example 1: Using the quadratic formula | Quadratic equations | Algebra I | Khan Academy