9.5 - Solving systems with linear and quadratic functions

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution if it satisfies all equations in the system.

Front

How do you solve a system of linear and quadratic equations?

Back

Set the equations equal to each other and solve for the variable.

Front

What is the first step in solving the system: y = x^2 + 3x - 5 and y = x + 3?

Back

x^2 + 3x - 5 = x + 3.

Front

What is the vertex of a quadratic function?

Back

The highest or lowest point of the parabola, found at x = -b/(2a) for the equation ax^2 + bx + c.

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does it mean for two equations to intersect?

Back

They have at least one solution in common, represented by the point(s) where their graphs meet.

Front

What is the discriminant in a quadratic equation?

Back

The value b² - 4ac that determines the nature of the roots: two real, one real, or no real roots.

Front

How can you graph a quadratic function?

Back

Plot the vertex, axis of symmetry, and additional points, then draw a parabola.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, represented by the value of y when x = 0.