1.6 Quadratics - Finding the Solutions From a Graph

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.

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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'.

Tags

CCSS.HSF-IF.C.7A

Front

What are the zeros of a quadratic function?

Back

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.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

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.

Front

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?

Back

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.

Tags

CCSS.HSF-IF.C.7A

Front

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

Back

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.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Front

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

Back

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?

Back

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

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, and it passes through the vertex.