Standard Form

Quadratic Formula's and Completing The Square

Learning goals

1)You will learn to find the X-intercepts by using an quadratic equation from a parabola.

2)How to use the given terms to find a full equation.

3)What to do in a situation where only the vertex is given with a parabola.

What are Quadratic Formula's?

Well the quadratic formula is:
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The quadratic formula is used to find any x-intercept of a parabola.

There are values in the formula (a, b and c) these are all in a a quadratic equation

A standard form for quadratic equation is


y=ax^2+bx+c

ax^2+bx+c becomes a(x-h)^2+k
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The first step was using the a, b and c terms from the standardized equation.

The second step was substituting the variables into the quadratic equation form.

The next step to solve.


you are left with 2 x-intercepts.

Solving quadratic equations by completing the square | Algebra II | Khan Academy

What is a Discriminant?

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

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

If D=0, there are no x-intercepts.

In every quadratic formula there is a discriminant of #

The discriminant can be represented by:


In quadratic formula's there are these equations called a discriminant.

The discriminant is:

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Word Problem

Matthew is selling Elite Limited edition sports cards to Hockey, Basketball and Baseball playing fans after their league games. His regular price per card is $10 and he averages of 20 cards per game. Matthew has realized that every reduction of $0.50 he can sell on average 1 more photograph.


a)Write an equation to represent Matthew's total sales revenue.

[R=(Price)(Quantity)]

Let X represent the amount of price by decrease.

Equation:

R=(20-0.50x)(10+x)


b) What price must Matthew charge in order to maximize the total profits.

R=(20-0.50x)(10+x)

=200 + 20x - 5x - 0.5x^2 15/2=-7.5 7.5^2=56.25

=-(0.5x^2+15x) + 200

=-(0.5x^2 - 15x) + 200

=-(0.5x^2 - 15x + 56.25 - 56.25) + 200

=-(0.5x^2 - 15x + 56.25) + 200 + 56.25

=-(0.5^2 - 7.5)^2 + 256.25

This becomes a vertex of (7.5, 256.25)

Price= 10 - 0.50x

=10 - 0.50(7.5)

=10 - 3.75

= 6.25

Therefore, To get top dollar for his revenue. Matthew must charge $6.25 per card.