# Standard Form

### Quadratic Formula, and Completing the square

## Learning Goals

1) You will learn how to find the x intercepts of a parabola using the quadratic formula.

2) You will learn how to complete the square in order to find the vertex of a parabola.

## Summary

**What is the quadratic formula?**

**The quadratic formula is**

The quadratic formula is used to find the x intercepts of a parabola.

The values for the variables a,b, and c are taken from standard form quadratic equation.

**The standard form quadratic equation is**

y=ax^2+bx+c

Inside the quadratic formula, there is something called the discriminant.

**The discriminant is**

**If D=0, there is only 1 x-intercept.**

**If D>0, there are 2 x-intercepts.**

**If D<0, there are no x-intercepts.**

**What is Completing the square?**

Completing the square is the method in which the standard form quadratic equation is turned into the vertex form quadratic equation to find the vertex of the parabola.

**ax^2+bx+c ----> a(x-h)^2+k**

## Example of Quadratic Formula

They were then substituted into the respective variables in the quadratic formula.

Now to solve.

You can see that 2 x-intercepts were found. You can see this because the discriminant was a greater than 0.

## Example of Completing the Square

y=2x^2+16x-3 was turned into the vertex form quadratic equation y=2(x+4)^2-35.

This allows us to find the vertex of this parabola, which is (-4,-35).

## Word Problem (Completing the Square)

A ball was thrown from a ladder. The equation that the ball makes when thrown is y=-5x^2+10x+1. The height is represented by h in metres, and time is represented by x in seconds. What is the maximum height the ball reached, and what time did the ball reach this height?

y=-5x^2+10x+1 (-2/2)^2 = -1^2 = 1

y=(-5t^2+10x)+1

y=-5(x^2-2x)+1

y=-5(x^2-2x+1-1)+1

y=-5(x^2-2x+1)+1+5

y=-5(x^2-2x+1)+6

y=-5(x-1)^2+6

h=1, k=6

Therefore the ball reached the maximum height of 6 metres after 1 second.