Ch4 First Half - Vertex/Standard/Intercept Factoring GOOD

Front

What is the standard form of a quadratic function?

Back

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

Front

How does the value of 'a' in a quadratic function affect its graph?

Back

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

Front

What is the vertex of a parabola in standard form?

Back

The vertex of a parabola in standard form f(x) = ax^2 + bx + c can be found using the formula x = -b/(2a).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What does the y-intercept of a quadratic function represent?

Back

The y-intercept is the point where the graph intersects the y-axis, represented by the value of c in the standard form f(x) = ax^2 + bx + c.

Front

How can you determine if a quadratic function opens upward or downward?

Back

A quadratic function opens upward if the coefficient 'a' is positive and downward if 'a' 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 do you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting the quadratic equation f(x) = 0 and solving for x using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant of a quadratic equation tell you?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.