1.6 Quadratics - Finding the Solutions From a Graph

Front

What is a quadratic function?

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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.

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What does the graph of a quadratic function look like?

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

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What are the zeros of a quadratic function?

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The zeros of a quadratic function are the values of x for which the function f(x) = 0. They represent the points where the graph intersects the x-axis.

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How can you find the number of solutions of a quadratic equation from its graph?

Back

The number of solutions corresponds to the number of times the graph intersects the x-axis: 0 intersections means no real solutions, 1 intersection means one real solution, and 2 intersections mean two real solutions.

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What does it mean if a quadratic function has two solutions?

Back

If a quadratic function has two solutions, it means the graph intersects the x-axis at two distinct points, indicating two different x-values that satisfy the equation.

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What does it mean if a quadratic function has one solution?

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If a quadratic function has one solution, it means the graph touches the x-axis at exactly one point (the vertex), indicating a repeated root.

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

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If a quadratic function has no real solutions, it means the graph does not intersect the x-axis at all, indicating that the solutions are complex or imaginary.

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How can you determine the vertex of a quadratic function from its graph?

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The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

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What is the significance of the vertex in a quadratic function?

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The vertex represents the maximum or minimum value of the quadratic function and is crucial for understanding the function's behavior.

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What is the axis of symmetry in a quadratic function?

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The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, and it passes through the vertex.