Unit 8: Introduction to Quadratics Review

y=x²

Quadratic functions form a "u" shaped graph called a parabola

All quadratics are based off of the parent function y=x²

if a=1 then the parabola follows a standard pattern when graphed

The turning point or tip of our parabola

The vertex is either a maximum or minimum depending on the direction of our parabola

Goes through the center of the parabola

Always goes through the vertex

x=h or x=-b/2a

Point that touches/crosses the y-axis

X-coordinate is 0

Point(s) that touches/crosses the x-axis

Y-coordinate is 0

Also known as zeros or solutions

If the vertex is below the x-axis, there will be two x-intercepts

If the vertex is on the x-axis, there will be one x-intercept

If the vertex is above the x-axis, there will be no x-intercepts

Standard Form is a trinomial

The most visible point while in standard form is the y-intercept

We can use the formula x=-b/2a to find the axis of symmetry

We can use this to also find the x-coordinate and y-coordinate of our vertex

Vertex form is written as a binomial term squared plus an integer

We can easily see our vertex in vertex form

If a is positive (+) then it is CONCAVE UP (smiling) and has a MINIMUM

If a is negative (-) then it is CONCAVE DOWN (frowning) and has a MAXIMUM

Use either area model or distribution method

Multiply all terms together

Combine like terms to simplify

Use either area model or distribution method

Multiply all terms together

Combine like terms to simplify