4. Polynomial Functions

Quadratic Functions

4. Polynomial Functions

Quadratic Functions

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Multiple Choice

Where is the axis of symmetry located on the given parabola?

$x=3$

$x=0$

$x=1$

$x=4$

Verified step by step guidance

Identify the vertex of the parabola on the graph. The vertex is the point where the parabola changes direction, and it appears to be at (3, 0) on this graph.

Understand that the axis of symmetry of a parabola is a vertical line that passes through the vertex. For a parabola in the form y = ax^2 + bx + c, the axis of symmetry can be found using the formula x = -b/(2a).

Since the vertex is at (3, 0), the axis of symmetry is a vertical line passing through x = 3.

Verify the symmetry by observing that the parabola is mirrored on either side of the line x = 3. Points on the parabola equidistant from x = 3 should have the same y-values.

Conclude that the axis of symmetry for the given parabola is x = 3, as it divides the parabola into two mirror-image halves.

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A quadratic equation ƒ(x) = 0 has a solution x = 2. Its graph has vertex (5, 3). What is the other solution of the equation?

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Textbook Question

In Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-4) The graph passes through the point (1,4).

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In Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-1) The graph passes through the point (-2,-3).

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Multiple Choice

Identify the ordered pair of the vertex of the parabola. State whether it is a minimum or maximum.

Graph the given quadratic function. Identify the vertex, axis of symmetry, intercepts, domain, range, and intervals for which the function is increasing or decreasing. $f\left(x\right)=-\left(x-5\right)^2+1$

Graph the given quadratic function. Identify the vertex, axis of symmetry, intercepts, domain, range, and intervals for which the function is increasing or decreasing. $f\left(x\right)=3x^2+12x$