Quadratic Key Features

Front

What is a quadratic function?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 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 of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

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How do you find the axis of symmetry of a parabola?

Back

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

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What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph intersects the x-axis, also known as the zeros or roots of the function.

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What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

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What does it mean if a quadratic equation has two real solutions?

Back

It means the graph of the quadratic function intersects the x-axis at two distinct points.

Front

What does it mean if a quadratic equation has one real solution?

Back

It means the graph of the quadratic function touches the x-axis at exactly one point, known as a double root.

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What does it mean if a quadratic equation has no real solutions?

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It means the graph of the quadratic function does not intersect the x-axis at all, indicating that the roots are complex.