Quadratics Forms and Parabolas Key Features

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 axis of symmetry for a parabola?

Back

The axis of symmetry for a parabola in the form y = ax^2 + bx + c is given by the formula x = -b/(2a). This line divides the parabola into two mirror-image halves.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is given by y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

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

Back

The 'a' value in a quadratic equation determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

What is the significance of the 'h' and 'k' values in vertex form?

Back

In the vertex form y = a(x - h)^2 + k, 'h' represents the x-coordinate of the vertex, and 'k' represents the y-coordinate of the vertex.

Front

How can you convert from vertex form to standard form?

Back

To convert from vertex form y = a(x - h)^2 + k to standard form y = ax^2 + bx + c, expand the equation and simplify.

Front

What is the formula for finding the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0, which gives the point (0, c) in standard form y = ax^2 + bx + c.

Front

What is the relationship between the roots of a quadratic equation and its graph?

Back

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

Front

What is the quadratic formula?

Back

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