Parts of a Parabola

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the point where the parabola changes direction. It is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the vertex of a parabola given its equation in standard form?

Back

For a parabola in standard form y = ax^2 + bx + c, the vertex can be found using the formula: x = -b/(2a). Substitute this x-value back into the equation 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. It passes through the vertex and is given by the equation x = h, where h is the x-coordinate of the vertex.

Front

How do you determine the axis of symmetry from the vertex of a parabola?

Back

The axis of symmetry can be determined from the vertex (h, k) as the line x = h.

Front

What are the roots of a parabola?

Back

The roots of a parabola are the x-values where the parabola intersects the x-axis. These are the solutions to the equation when y = 0.

Front

How can you find the roots of a quadratic equation?

Back

Roots can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients from the quadratic equation ax² + bx + c = 0.

Front

What does the discriminant of a quadratic equation tell you about the roots?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root (a repeated root); if D < 0, there are no real roots.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How can you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, you can complete the square on the quadratic expression.