Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

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

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation in standard form.

Front

What are the zeros of a quadratic function?

Back

The zeros (or roots) of a quadratic function are the x-values where the function equals zero, which can be found by factoring, using the quadratic formula, or graphing.

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What is the quadratic formula?

Back

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

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What does it mean for a parabola to open upwards?

Back

A parabola opens upwards when the coefficient 'a' in the quadratic function f(x) = ax² + bx + c is positive, indicating a minimum point at the vertex.

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What does it mean for a parabola to open downwards?

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A parabola opens downwards when the coefficient 'a' is negative, indicating a maximum point at the vertex.

Front

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

Back

If 'a' is positive, the function has a minimum value; if 'a' is negative, it has a maximum value.

Front

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

Back

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