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MariettaO [177]
1 year ago
13

- Polynomial Functions -For each function, state the vertex; whether the vertex is a maximum or minimum point; the equation of t

he axis of symmetry and whether the function's graph is steeper than, flatter than, or the same shape as the graph of f(x)=x²

Mathematics
1 answer:
vladimir2022 [97]1 year ago
3 0

EXPLANATION

Given the function f(x) = (x-6)^2 + 1

\mathrm{The\: vertex\: of\: an\: up-down\: facing\: parabola\: of\: the\: form}\: y=ax^2+bx+c\: \mathrm{is}\: x_v=-\frac{b}{2a}

Expanding (x-6)^2 + 1 by applying the Perfect Square Formula:

=x^2-12x+37\mathrm{The\: parabola\: params\: are\colon}a=1,\: b=-12,\: c=37x_v=-\frac{b}{2a}x_v=-\frac{\left(-12\right)}{2\cdot\:1}\mathrm{Simplify}x_v=6y_v=6^2-12\cdot\: 6+37

Simplify:

y_v=1

\mathrm{Therefore\: the\: parabola\: vertex\: is}\mleft(6,\: 1\mright)\mathrm{If}\: a\mathrm{If}\: a>0,\: \mathrm{then\: the\: vertex\: is\: a\: minimum\: value}a=1\mathrm{Minimum}\mleft(6,\: 1\mright)\mathrm{For\: a\: parabola\: in\: standard\: form}\: y=ax^2+bx+c\: \mathrm{the\: axis\: of\: symmetry\: is\: the\: vertical\: line\: that\: goes\: through\: the\: vertex}\: x=\frac{-b}{2a}

Expanding (x-6)^2 + 1 by applying the Perfect Square Formula:

y=x^2-12x+37\mathrm{Axis\: of\: Symmetry\: for}\: y=ax^2+bx+c\: \mathrm{is}\: x=\frac{-b}{2a}a=1,\: b=-12x=\frac{-\left(-12\right)}{2\cdot\:1}\mathrm{Refine}

Axis of simmetry : x=6

The quadratic function has the same shape than the parent function y=x^2 because there is NOT a coefficient within x.

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<h3>Number of Street Boards in the Budget</h3>

The number of streets boards that can be produced in the budget is calculated by dividing the total amount budgeted by the cost of each street board. This is done mathematically as

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Learn more on division of numbers here;

brainly.com/question/20301788

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