Max and Min Parabolas

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped curve that represents the graph of a quadratic function.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in a quadratic function indicate?

Back

The 'a' value determines the direction of the parabola: if 'a' is positive, the parabola opens upwards (minimum); if 'a' is negative, it opens downwards (maximum).

Front

How do you find the vertex of a parabola?

Back

The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting this value back into the function to find the y-coordinate.

Front

What is the axis of symmetry in a parabola?

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 maximum value of a parabola that opens downwards?

Back

The maximum value is the y-coordinate of the vertex of the parabola.

Front

What is the minimum value of a parabola that opens upwards?

Back

The minimum value is the y-coordinate of the vertex of the parabola.

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

You can determine this by looking at the 'a' value: if 'a' is positive, it has a minimum; if 'a' is negative, it has a maximum.

Front

What is the y-intercept of a quadratic function?

Back

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

Front

How do you find the roots of a quadratic function?

Back

The roots can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).