Graphing Quadratic Functions Flashcard

Front

What does the value of 'a' in a quadratic equation indicate about the direction of the parabola?

Back

The value of 'a' tells you the direction of the opening: if 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.

Front

How do you find the vertex of a quadratic function in standard form?

Back

To find the vertex of a quadratic function in the form y = ax^2 + bx + c, use the formula x = -b/(2a) to find the x-coordinate, then substitute this value back into the equation to find the y-coordinate.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, which occurs when x = 0.

Front

How can you determine the y-intercept from the equation y = ax^2 + bx + c?

Back

The y-intercept is given by the constant term 'c' in the equation.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the vertex of the quadratic function y = x^2 + 16x + 71?

Back

The vertex is V(-8, 7).

Front

How do you find the y-intercept of the function y = x^2 - 6x + 5?

Back

Substituting x = 0 into the equation gives y = 5, so the y-intercept is (0, 5).

Front

What does it mean if a parabola opens downward?

Back

If a parabola opens downward, it indicates that the coefficient 'a' in the quadratic equation is negative.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on whether it opens upward or downward.

Front

How can you tell if a parabola opens to the left or right?

Back

A parabola opens to the left or right if it is in the form x = ay^2 + by + c, where 'a' determines the direction.