Explore Quadratic Functions and Their Properties

Front

What is the Binomial Expansion of \( (x+5)^{2} \)?

Back

\( x^{2} + 10x + 25 \)

Front

What is the vertex of the function \( f(x) = -2(x+6)^{2} - 7 \)?

Back

(-6, -7)

Front

Find the axis of symmetry of the quadratic \( y = -2x^{2} + 8x + 10 \).

Back

x = 2

Front

Complete the square and write in Vertex Form for \( f(x) = x^{2} + 4x + 9 \).

Back

\( f(x) = (x+2)^{2} + 5 \)

Front

Using Vertex Form, \( f(x) = a(x - h)^{2} + k \), how do you write the equation for the Axis of Symmetry?

Back

x = h

Front

What is a quadratic function?

Back

A polynomial function of degree 2, typically in the form \( f(x) = ax^{2} + bx + c \).

Front

What does the 'a' in a quadratic function determine?

Back

The direction of the parabola (opens upwards if a > 0, downwards if a < 0).

Front

What is the standard form of a quadratic function?

Back

\( f(x) = ax^{2} + bx + c \) where a, b, and c are constants.

Front

What is the vertex form of a quadratic function?

Back

\( f(x) = a(x - h)^{2} + k \) where (h, k) is the vertex.

Front

How do you find the y-intercept of a quadratic function?

Back

Set \( x = 0 \) and solve for \( f(0) \).