Quadratic Functions

Front

What are the x-intercepts of the function f(x)= (x - 2)(x + 3)?

Back

x = 2 or x = -3

Front

How many solutions does the graph of a quadratic function have if it does not intersect the x-axis?

Back

no solutions

Front

The solutions of a quadratic equation are known as the _____?

Back

Roots

Front

What is the vertex form of the quadratic function f(x) = (x - 2)² - 4?

Back

f(x) = (x - 2)² - 4

Front

What transformations are applied to the parent function y = x² in g(x) = -1/5(x - 1)² + 7?

Back

reflection, vertical compression, horizontal right, vertical up

Front

What is the standard form of a quadratic function?

Back

f(x) = ax² + bx + c

Front

How do you find the vertex of a quadratic function in standard form?

Back

Use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What does the discriminant of a quadratic equation tell us?

Back

It indicates the nature of the roots: positive for two real roots, zero for one real root, and negative for no real roots.

Front

What is the axis of symmetry for the quadratic function f(x) = ax² + bx + c?

Back

x = -b/(2a)

Front

How can you determine if a quadratic opens upwards or downwards?

Back

If a > 0, it opens upwards; if a < 0, it opens downwards.