# Quadratics

### 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

## 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

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