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 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
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 Equ. #4:

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 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

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 Ineq. #9:

 Solve for:

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DEFINITION.
A quadratic function is a polynomial of degree 2:

The graph is a parabola.
• If a > 0, the horns point up.

If a < 0, the horns point down.

If |a| > 1, the parabola is narrower than y = x2.

If |a| < 1, the parabola is wider than y = x2.

Determine the shape of the following graphs. Pick the
shape below.

Given
Get the roots by factoring or using the quadratic formula:
. No roots if

COMPLETING THE SQUARE THEOREM. Every quadratic
function may be written in the form:

where is the vertex (or nose) of the parabola.

Proof. Given

• Factor the a out of the ax2+bx part.

• Divide the new coefficient of x by 2 and square.
Add this to complete the square.

• Anything which is added must also be subtracted to
preserve equality.

• Find the roots (the roots are the x-intercepts).

• Write in completed square form:

• Graph. On the graph list both coordinates of the vertex.

Find the vertex.

Find the graph with the correct shape and position.

Find the roots. x = ?, ?
Write equation in the form:

Find the vertex.

WORD PROBLEMS

• Draw the picture. Indicate the variables in the picture.
• Write the given equations which relate the variables.
• Solve for the wanted quantities.

The perimeter of a rectangle is 10 feet.
Express the area A in terms of the width x.

The area of a rectangle is 10 square feet.
Express the perimeter P in terms of the width x.

List the given.

Write the perimeter as a function of x

The corner of a triangle lies on the line

Express the triangle’s area and perimeter in terms of the
base x.

The area of an isosceles triangle is 16.

Write the triangle’s height h in terms of its width w.

Write the triangle’s width w in terms of its height h.

The curved surface
area is the area of the
can’s side, excluding
the top and bottom

The height of a can (right circular cylinder)