Warm Up 12/02/2024 Key Features of Quadratics

Front

What is the range of a quadratic function?

Back

The range of a quadratic function is the set of possible output values (y-values). For a parabola that opens upwards, the range is from the minimum value to positive infinity. For example, if the vertex is at (0, -2), the range is [-2, +∞).

Front

What are x-intercepts in a quadratic function?

Back

X-intercepts are the points where the graph of the quadratic function crosses the x-axis. They are found by setting the function equal to zero and solving for x. For example, if the function is y = x^2 - 4, the x-intercepts are x = 0 and x = 4.

Front

What is the difference between maximum and minimum values in quadratics?

Back

A maximum value is the highest point on the graph of a quadratic that opens downwards, while a minimum value is the lowest point on the graph of a quadratic that opens upwards.

Front

What is a decreasing interval in a quadratic function?

Back

A decreasing interval is a range of x-values where the function's output (y-value) decreases as x increases. For example, in the function y = -x^2 + 4, the interval (-∞, 0) is decreasing.

Front

How do you determine if a quadratic function has a maximum or minimum value?

Back

You can determine this by looking at the direction of the parabola. If it opens upwards, it has a minimum value; if it opens downwards, it has a maximum value.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards. It can be found using the formula x = -b/(2a) for the quadratic equation ax^2 + bx + c.

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. It passes through the vertex and can be found using the formula x = -b/(2a).

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is written as f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the 'a' value in a quadratic function indicate?

Back

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

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of the quadratic equation. If it's positive, there are two real roots; if zero, one real root; if negative, no real roots.