Unit 9 Writing and Solving Quadratic Equations

quadratic term

A term of degree two

Real Roots/Real Solutions

Can be found where the graph crosses the x-axis

Zeros of a quadratic equation

Points where the graph crosses the x-axis where the y-coordinate of the point is zero; (x, 0)

Quadratic Equation

Polynomial with degree 2

A quadratic equation will have two real solutions when...

The graph crosses the x axis in two places

Parabola

The shape of a the graph of a quadratic function

minimum value of a function

The y-value of the point where the graph changes from decreasing to increasing

Vertex Form

a way of writing a quadratic equation such that the vertex (h, k) is identifiable in the equation

standard form of a quadratic equation

ax² + bx + c = 0 such that a cannot be equal to zero

Discrminant

b^2-4ac

intercept form of a quadratic equation

the form y = a(x - p)(x - p), where the x-intercepts of the graph are p and q

quadratic formula

the formula used to find the solutions of a quadratic equation

maximum value of a function

the greatest y-value of a function

vertex of a parabola

the highest or lowest point on the graph

axis of symmetry

the line that cuts the graph into two symmetrical parts

A quadratic equation will have no real solutions when...

the parabola does not cross the x axis

x-intercept

the point where a graph crosses the x-axis

y-intercept

the point where the graph crosses the y-axis

factored form quadratic

the product of a constant and two linear terms

A quadratic equation will have one real solution when...

the vertex of the parabola is on the x axis

Zero Product Property

When the product of two or more factors is zero, one of the factors must equal zero.