Quadratics Math Concept Map

Quadratic Relations

Which includes

Vertex Form

y = a(x-h)² + k

The VERTEX(h,k)

Translations, which can be either

y = a(x-h)² + k , the h-value is the vertical translation

y = a(x-h)² + k , the k-value is the horizontal translation

a-value

The parabola will face downwards

The parabola will face upwards

Transformations

The parabola is compressed

The parabola is stretched

More specific on how much the parabola is being compressed or stretched, use the equation, "1a,3a,5a". Substitute the a-values into the equation, as shown below.

Standard Form

y = ax² + bx + c

complete the square if a=1

y = x² - 6x +4
y = (x² - 6x) +4
y = (x² - 6x + 9 - 9) +4
y = (x²- 6x + 9) - 9 + 4
y = (x-3)² - 5

The first blue Line is the standard form.The next line shows how the x variables are grouped. After grouping the x variables divide the middle coefficient by two, square the result, than add and subtract the number inside the brackets.Remove the subtracted term, from the brackets.Factor the brackets as a perfect square trinomial. Remember to solve whats outside the brackets as well. This is the result of factoring the standard form, which is now the vertex form.

complete the
square if a ≠1

y = 2x² - 16x -1
y = (2x² - 16x) - 1
y = 2(x² - 8x) - 1
y = 2(x²- 8x + 16 - 16) - 1
y = 2(x² - 8x + 16) - 16(2) - 1
y = 2(x - 4)² - 33

The first blue Line, is the standard form when a ≠1. Group the x-terms as shown in the red line. Common factor just the a-value from the x-terms. Divide the coefficient of the middle term by 2, square it,
then add and subtract that number inside the brackets. Remove the subtracted term from the brackets. Multiply it by the "a" value you factored out. Factor the brackets as a perfect square trinomial.

X-intercept/Factored Form

y = a(x-p)(x-q)

can also be changed into Standard form

You can complete the square.

Parabola

Key features

Zeroes

Zeros are
where a
parabola
cross the
x-axis. A
parabola
may have
one,two,
or no
zeros

Maximum and minimum

through a chart using second differences

Second differences, can assists with figuring our whether there is a linear relation, a quadratic relation, or neither.

y = x²

y = x² points to the coordinates
(0,0), which is the origin of the
Cartesian plane. The parabola
faces upwards.

Completing
the square
refers to
factoring a
perfect square
trinomial to get
the square
of a binomial

By using the QUADRATIC FORMULA

The Axis of symmetry

Optimal value

The optimal value
represents the
y-coordinate

The axis of symmetry
is a vertical line that
separates the parabola into
two congruent halves.

Floating topic