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3 years ago

P(x) = 2x² + 1 What is the inverse for p(x)?

Mathematics

1 answer:

Serhud [2]3 years ago

4 0

Answer:

$P^{-1} (x)=\sqrt{\frac{x-1}{2} }$

Step-by-step explanation:

1. $P(x)=2x^{2} +1$

2. $y=2x^{2} +1$

3. $x=2y^{2} +1$

4. $2y^{2} =x-1$

5. $y^{2} =\frac{x-1}{2}$

6. $y=\sqrt{\frac{x-1}{2} }$

7. $P^{-1} (x)=\sqrt{\frac{x-1}{2} }$

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3 years ago

Y = – 2x² + 12x - 7

Vikentia [17]

Answer:

a) axis of symmetry: <em> </em><em>x</em> = <em>h</em>

b) Vertex: (3, 11).

c/d) Maximum point = vertex (3, 11).

Step-by-step explanation:

<em><u>Note:</u></em><em> </em>This post will only provide the answers for parts a through d, in accordance with Brainly's Guidelines.

Given the quadratic equation, y = – 2x² + 12x - 7, where a = -2, b = 12, and c = -7:

<h3> </h3><h3>a) What is equation of the axis of symmetry?</h3>

The <u>axis of symmetry</u> is an imaginary line that divides the graph of a parabola into two symmetrical parts. The axis of symmetry goes through the x-coordinate of the vertex, (<em>h</em>, k). Hence, the axis of symmetry is often represented by the following equation: x = h.

<h3 /><h3>b) What is the vertex?</h3>

We can find the x-coordinate of the vertex by using the following formula:

$\displaystyle\mathsf{x\:=\:\frac{-b}{2a}}$

Substitute the given values for a = -2, and b = 12 into the formula:

$\displaystyle\mathsf{x\:=\:\frac{-(12)}{2(-2)}\:=\:\frac{-12}{-4}\:=\:3}$

Hence, the x-coordinate of the vertex is 3.

Substitute x = 3 into the given quadratic equation to find its corresponding y-coordinate:

y = – 2x² + 12x – 7

y = – 2(3)² + 12(3) – 7

y = –2(9) + 36 – 7

y = – 18 + 36 – 7

y = 11

Therefore, the <u>vertex</u> of the given quadratic equation is (3, 11).

<h3 /><h3>c/d) Does the equation have a maximum or minimum? What is the maximum/minimum?</h3>

The value of the "<em>a</em>" coefficient in the quadratic equation, y = <u>a</u>x² + bx + c, determines whether a given parabola has either a minimum, or a maximum.

If <em>a</em> > 1, then it means that the graph of a parabola opens <u>upward</u>, and the vertex is its <u><em>minimum</em></u> point.

If <em>a</em> < 0, then the graph of a parabola opens downward, and the vertex is its <u><em>maximum</em></u> point.

Since the value of our given quadratic equation is a = -2, then it means that its graph opens <em>downward</em>, and that the <u>vertex is its maximum point</u>.

Attached is a screenshot of the graph, where it shows the vertex occurring at point (3, 11), for which the axis of symmetry goes through at x = 3.

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2 years ago