Quadratic Functions Key Features Warmup 2

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on whether it opens upwards or downwards.

Front

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

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating f(0).

Front

What are x-intercepts in a quadratic function?

Back

X-intercepts are the points where the graph crosses the x-axis, found by solving the equation f(x) = 0.

Front

What does it mean if a quadratic function has a maximum value?

Back

A maximum value occurs when the parabola opens downwards, indicating the vertex is the highest point on the graph.

Front

What does it mean if a quadratic function has a minimum value?

Back

A minimum value occurs when the parabola opens upwards, indicating the vertex is the lowest point on the graph.

Front

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

Back

If the coefficient 'a' in the quadratic function f(x) = ax² + bx + c is positive, it opens upwards; if 'a' is negative, it opens downwards.