**Quadratics**

**Solving**

Solve

Calculators are sold to students for 20 dollars each. Three hundred students are willing to buy them at that price. For every 5 dollar increase in price, there are 30 fewer students willing to buy the calculator. What selling price will produce the maximum revenue?

Solve

Find the value of K for which the equation x+Kx+9=0 has two different, real roots.

Solve

1. A matte of uniform width is to be placed around a painting so that the area of the matted surface is twice the area of the picture. If the outside dimensions of the matte are 40cm and 60cm, ﬁnd the width of the matte around the picture.

2. A parabola passes the x-axis at -4 and 20 and has a y-intercept of 8. Determine the equation of the function.

Solve a problem arising from a realistic situation represented by a graph or an equation of a quadratic relation.(Word problems) -- > Revenue, Dimensions, Etc.

Creating quadratic equations with the information given.

Your turn

MATH

Learning Goals:

1.

Solving quadratic equations by factoring or using quadratic formula

2.

Solving problems arising from a realistic situation represented by a graph or an equation of a quadratic relation.(Word problems) -- > Revenue, Dimensions, Etc.

3.

Creating quadratic equations with the information given.

Solve

Solve quadratic equation

3 (x+2)^2-21=0

Vocabulary

Solve

Creating quadratic equations with the information given.

Find two consecutive even integers whose product is 168.

Completing the Square:

A process for expression

y = ax^2 + bx + c

in the form

y = a(x-h)^2 + k

Quadratic Relations:

A relation whose equation is in the form

y = ax^2 + bx + c

, where

a

,

b

, and

c

, are real numbers and a

does not

equal 0.

Quadratic Formula:

A formula for determining the roots of a quadratic equation of the form

ax^2 + bx + c = 0

Roots:

The value of the variable that makes an equation true. The same as the solution of an equation.

Zeroes:

A value for x, or the independent variable, for which the defendant variable has value of 0. It corresponds to the x-intercept of the graph of the relation

X-intercept:

The x co-ordinate of the point where a line or a curve crosses the x-axis, at this point y = 0.

Quadratic Equation:

An equation in the form

ax^2 + bx + c = 0

, where b, and c, are real numbers, and a ≠ 0.

Solution:

The value of the variable that makes an equation true. The same as the root of the equation.

Discriminant:

Gives an idea of the number of roots and the nature of roots of the equation. If

ax^2 + bx + c = 0

is a quadratic equation, then the discriminant of the equation, ie.

D = B2-4ac

Inadmissible:

Not accepted as valid.

3(x+2)-21=0