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forsale [732]
3 years ago
12

The graph of y = x^2 -2x -3

Mathematics
1 answer:
KatRina [158]3 years ago
8 0

Answer:

See below

Step-by-step explanation:

A) Recall that a turning point is where the function changes from increasing to decreasing or vice versa. Since the graph of the function is a parabola, it only has 1 turning point, which is the vertex, or (1,-4). Therefore, the coordinates of the turning point are (1,-4).

B) The roots of the equation can be found by determining where the graph intercepts the x-axis (aka. x-intercepts). In this case, these are points (-1,0) and (3,0).

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Step-by-step explanation:

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3 years ago
Hey, I need help with questions 1 and 2, if anyone can help, please? thanks!
Eva8 [605]

The correct works are:

  • Blue(s + h) = 2s^2 + 4sh + 2h^2 + 3.
  • \frac{Blue(s + h) - Blue(s)}{h} = 4s + 2h

<h3>Function Notation</h3>

The function is given as:

Blue(s) = 2s^2 + 3

The interpretation when Steven is asked to calculate Blue(s + h) is that:

Steven is asked to find the output of the function Blue, when the input is s + h

So, we have:

Blue(s + h) = 2(s + h)^2 + 3

Evaluate the exponent

Blue(s + h) = 2(s^2 + 2sh + h^2) + 3

Expand the bracket

Blue(s + h) = 2s^2 + 4sh + 2h^2 + 3

So, the correct work is:

Blue(s + h) = 2s^2 + 4sh + 2h^2 + 3

<h3>Simplifying Difference Quotient</h3>

In (a), we have:

Blue(s + h) = 2s^2 + 4sh + 2h^2 + 3

Blue(s) = 2s^2 + 3

The difference quotient is represented as:

\frac{f(x + h) - f(x)}{h}

So, we have:

\frac{Blue(s + h) - Blue(s)}{h} = \frac{2s^2 + 4sh + 2h^2 + 3 - 2s^2 - 3}{h}

Evaluate the like terms

\frac{Blue(s + h) - Blue(s)}{h} = \frac{4sh + 2h^2}{h}

Evaluate the quotient

\frac{Blue(s + h) - Blue(s)}{h} = 4s + 2h

Hence, the correct work is:

\frac{Blue(s + h) - Blue(s)}{h} = 4s + 2h

Read more about function notations at:

brainly.com/question/13136492

4 0
2 years ago
En una granja se crían gallinas y conejos. Si se cuentan las cabezas son 50, si se cuentan las patas son 134. ¿Qué sistema de ec
svp [43]
Hay un total de 17 conejos y 33 gallinas
7 0
2 years ago
The positive difference of two integers is 13. The sum of the larger number and the square of the smaller is 103. Give your solu
nydimaria [60]

Answer:

(22, 9)

Step-by-step explanation:

The positive difference of two integers is 13. The sum of the larger number and the square of the smaller is 103. Give your solution(s) as ordered pair (larger, smaller).    I'll call the two integers a and b.

a - b  =  13        a + b² = 103

<u>   +b     +b</u>

a   =  13 + b    plug this into the second equation

a + b² = 103

(13+b) + b²  = 103    subtract 103 from both sides to get one side equal to zero

<u>-103              -103</u>

b² + b - 90 = 0      what factors (two numbers multiply) to -90 that also add up

                             to 1? The only two that work are -9 and 10.  

(b-9)(b+10) = 0      so  b-9 = 0     or    b+10 = 0

                                     <u>+9  +9</u>    or       <u>-10   -10</u>

                                     b = 9      or    b = -10 but both numbers must be positive

b = 9  and a = 13 + b so   a = 13 + 9 = 22

(22, 9)

5 0
4 years ago
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