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 graph, depending on whether it opens upwards or downwards.

Front

What shape do quadratic equations take when graphed?

Back

Quadratic equations take the shape of a parabola when graphed.

Tags

CCSS.HSF-IF.C.7A

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. For the parabola with vertex (h, k), the Axis of Symmetry is given by the equation x = h.

Front

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

Back

For a quadratic equation in standard form y = ax^2 + bx + c, the vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting this value back into the equation to find the y-coordinate.

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

What does the 'a' in the vertex form of a quadratic equation represent?

Back

In the vertex form y = a(x - h)² + k, the 'a' value determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis. It can be found by evaluating the function at x = 0.

Tags

CCSS.HSF-IF.C.7A

Front

How can you determine if a parabola opens upwards or downwards?

Back

You can determine the direction of a parabola by looking at the coefficient 'a' in the quadratic equation. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

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

Back

The vertex (h, k) of a parabola given in standard form y = ax^2 + bx + c can be found using h = -b/(2a) and k = f(h), where f(h) is the value of the quadratic function at x = h.

Front

What is the relationship between the vertex and the maximum or minimum value of a quadratic function?

Back

The vertex of a quadratic function represents the maximum value if the parabola opens downwards (a < 0) and the minimum value if it opens upwards (a > 0).