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
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.
• 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
• 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.
• 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
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)
is three times the radius.
Express the radius as a function
of the curved surface area.
The height of a can (right circular cylinder)
is four times the radius.
Express the curved surface area as a function
of the radius.