6.1-6.2 Flashcard Review of Quadratics

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

The value of 'a' determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. A larger absolute value of 'a' makes the parabola narrower.

Front

What is the quadratic parent function?

Back

The quadratic parent function is y = x².

Front

How do you determine if a quadratic function is wider or narrower than the parent function?

Back

Compare the absolute value of 'a' in the function y = ax². If |a| < 1, the graph is wider; if |a| > 1, it is narrower.

Front

What is the vertex of the quadratic function f(x) = (x + 3)² - 4?

Back

The vertex is (-3, -4).

Front

What is the axis of symmetry for the quadratic function f(x) = 2(x - 1)² + 3?

Back

The axis of symmetry is x = 1.

Front

What does it mean for a quadratic function to have a maximum value?

Back

A quadratic function has a maximum value if it opens downwards (when 'a' is negative) and the vertex represents the highest point on the graph.

Front

What does it mean for a quadratic function to have a minimum value?

Back

A quadratic function has a minimum value if it opens upwards (when 'a' is positive) and the vertex represents the lowest point on the graph.

Front

How can you find the y-intercept of a quadratic function?

Back

To find the y-intercept, set x = 0 in the quadratic equation and solve for y.

Front

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

Back

The vertex is the point where the graph changes direction and represents either the maximum or minimum value of the function.