Quadratic Basics

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. It passes through the vertex of the parabola.

Front

How do you find the axis of symmetry for a quadratic equation in standard form?

Back

For a quadratic equation in the form y = ax^2 + bx + c, the axis of symmetry can be found using the formula x = -b/(2a).

Front

What does it mean if a parabola opens upwards?

Back

A parabola opens upwards if the coefficient of x^2 (a) is positive. This means the vertex is the minimum point of the graph.

Front

What does it mean if a parabola opens downwards?

Back

A parabola opens downwards if the coefficient of x^2 (a) is negative. This means the vertex is the maximum point of the graph.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x where the graph intersects the x-axis. They can be found using factoring, completing the square, or the quadratic formula.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

How can you determine the direction a parabola opens from its equation?

Back

You can determine the direction by looking at the coefficient of x^2: if it's positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is a parabola?

Back

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