Key Characteristics of Quadratic Functions

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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 can be found using the formula x = -b/(2a) for a quadratic in the form ax^2 + bx + c.

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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 can be found by setting the quadratic equation equal to zero and solving for x.

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What does it mean if a quadratic function has a maximum vertex?

Back

A maximum vertex indicates that the highest point of the parabola is at the vertex, and the graph opens downwards.

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What does it mean if a quadratic function has a minimum vertex?

Back

A minimum vertex indicates that the lowest point of the parabola is at the vertex, and the graph opens upwards.

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How can you determine if a quadratic function opens up or down?

Back

The direction of the parabola is determined by the leading coefficient (a). If a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

What is the vertex of a quadratic function?

Back

The vertex is the point (h, k) where the parabola changes direction. It can be found using the formula h = -b/(2a) and k = f(h).

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What are the roots of a quadratic function?

Back

The roots (or solutions) are the values of x that make the quadratic equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

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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 is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if > 0, there are two real roots; if = 0, there is one real root; if < 0, there are no real roots.