Parabolas Introduction

Front

What is a parabola?

Back

A parabola is a U-shaped curve that is the graph of a quadratic function. It can open upwards or downwards.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it has a minimum value at its vertex.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it has a maximum value at its vertex.

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts are the points where the parabola crosses the x-axis, also known as the zeros of the function.

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, passing through the vertex.

Front

How can you determine the number of real solutions of a quadratic equation?

Back

The number of real solutions can be determined using the discriminant (b² - 4ac) from the quadratic formula. If it's positive, there are two solutions; if zero, one solution; if negative, no real solutions.

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 is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the formula to find the vertex of a parabola in standard form?

Back

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