Flashcard: Quadratic Systems/Vertex Form

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 coefficient 'a' in the quadratic equation y = ax² + bx + c determine?

Back

The coefficient 'a' determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Front

How do you find the height from which a projectile is launched using its height equation?

Back

To find the launch height, evaluate the height equation at t = 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert, complete the square on the quadratic equation.

Front

What are consecutive integers?

Back

Consecutive integers are integers that follow each other in order, such as -6 and -5.

Front

What is the vertex of the parabola given by the equation y = 3(x + 5)² - 4?

Back

The vertex is (-5, -4).

Front

What is the significance of the vertex in a parabola?

Back

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

Front

How do you determine the x-coordinate of the vertex from the standard form of a quadratic equation?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a) from the standard form y = ax² + bx + c.

Front

What is the product of two consecutive negative even integers that equals 24?

Back

The integers are -6 and -4.