# Unit 3: Standard Form

## Learning Goals

• I am able to use the quadratic formula in a quadratic equation
• I am able to use the standard form equations, to complete the square, and graph the parabola
• I am able to find the vertex using the complete the square formula
• I am able to find the x's using the quadratic formula
• I am able to find the discriminant using( D=b^2-4ac)
• I am able to graph the x-intercepts and the vertex, then draw a parabola

## Summary of the Unit

Standard Form Formula; y= ax^2+bx+c

• The value of c is the y-intercept
• The value of a shows you the shape of the parabola and the direction of opening (up or down)
• Solve using the quadratic formula, to get the x-intercepts
• Complete the square to get vertex form (max/min)

Discriminant:

• The formula b²-4ac in the quadratic formula is called the discriminant
• If b²-4ac then we will get two real solutions to the quadratic equation.
• If b²-4ac then we will get a double root to the quadratic equation.
• If b²-4ac then we will get two complex solutions to the quadratic equation.

Use the given equation to convert the equation into a standard equation, y=ax^2+bx+c. Then use your a,b and c to use the formula -b square root- 4ac over 2a, to substitute your a,b and c and solve for x, add one and minus one at the end, and you will have your x's.

## Completing the square example:

Use your standard equation, put first two digits into brackets, then divide b by 2, then square that (14/2=14^2=49), add 49 into the bracket an minus it and multiply it by what's infront of the bracket. Then add or subtract it by the number outside the bracket (c). and then square the brackets and you b and c will be your vertex.

## More About Standard Form to be Familiar With !

Writing Linear Equations: Standard Form