Which of the following statements are true about the equation below?

Mathematics

1 answer:

max2010maxim [7]3 years ago

8 0

Given: x^2 - 6x + 2

Statements:

1) The graph of the quadratic equation has a minimum value:TRUE. WHEN THE COEFFICIENT OF X^2 IS POSITIVE THE PARABOLA OPEN UPWARDS AND ITS VERTEX IS THE MINIMUM.

2) The extreme value is at the point (3 , - 7): TRUE

You have to find the vertex of the parabola:

x^2- 6x + 2 = (x - 3)^2 - 9 + 2 = (x - 3)^2 - 7 => vertex = (3, -7)

3) The extreme value is at the point (7, -3): FALSE. THE RIGHT VALUE WAS FOUND IN THE PREVIOUS POINT.

4) The solutions are x = - 3 +/- √7. FALSE.

Solve the equation:

(x - 3)^2 - 7 = 0 => (x - 3)^2 = 7 => (x - 3) = +/- √7 => x = 3 +/- √7

5) The solutions are x = 3 +/- √7. TRUE (SEE THE SOLUTION ABOVE).

6) The graph of the quadratic equation has a maximum value: FALSE (SEE THE FIRST STATEMENT).

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I need help with these two equations

Ivan

for these you need to rearrange the equations and do substitutions.

#3 = if x+y=5 then you know x = 5-y

now substitute that equation for x in the 2nd one so x + 2y = 8 becomes

5-y + 2y = 8 2y - y becomes 1y which becomes y then subtract 5 from each side to get y =3

now replace y with 3 in the first equation x = 5-3 so x = 2

so (2,3) is the answer

same type of work for #4

2x-y=6 ,S0 y = 2X+6

so now you have 4x+2(2x+6)=-4

that becomes 4x +4x+12 = -4

8x+8 = 1, x =1

y = 2(1)-6 = -4

so answer is (1,-4)

7 0

3 years ago

write a function g whose graph represents a translation 2 units to the right followed by a horizontal stretch by a factor or 2 o

Alenkinab [10]

$\bf f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}\\\\
f(x)=&{{ A}} \left|{{ B }}x+{{ C}} \right|+{{ D}}
\\\\
--------------------\\\\$

$\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the y-axis}$

$\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

with that template in mind, let's see,

$\bf f(x)=|x| \implies \begin{array}{lllccll}
f(x)=&1|&1x&+0|&+0\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}$

so, to shift it to the right by 2 units, simply set C = 2.
to stretch it by 2, set A = 1/2.

the smaller A is, the wider it opens, the larger it is, the more it shrinks.

5 0

3 years ago

Five-sixths of b is added to 7

Strike441 [17]

The answer would be 7+5/6b

5 0

3 years ago

Read 2 more answers

Can someone please help me

Nastasia [14]

Answer: I'm not to sure about this question its kind of confusing.

Step-by-step explanation: