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2 years ago

Which of the following statements about f(x)=(x-4)^2-1 are true? select all that apply

Mathematics

2 answers:

melamori03 [73]2 years ago

8 0

We have that
f(x)=(x-4)^2-1 in the question and f(x)=-(x-4)^2-1 in the picture
so

I'm going to analyze the two cases

using a graph tool

case 1)
f(x)=(x-4)^2-1
the vertex is the point (4,-1)
the x intercepts are the points (3,0) and (5,0)
the y intercept is the point (0,15)
the axis of symmetry is x=4
see the attached figure N 1

case 2)
f(x)=-(x-4)^2-1
the vertex is the point (4,-1)
there is no x intercepts
the y intercept is the point (0,-17)
the axis of symmetry is x=4
see the attached figure N 2

the answer
considering the case N 2 is
vertex (4,-1)------> is correct
y intercept (0,-17)-----> is correct
axis of symmetry x=4-----> is correct

Gre4nikov [31]2 years ago

6 0

Both the vertex being (4, -1) and the y-intercept being (0, 17) are true.

We can tell the vertex portion given the formula of a graph in vertex form: f(x) = (x - h) + k, where (h, k) is the vertex. This will show us that (4, -1) is the vertex.

We also know that the y intercept is -17 because when we plug 0 into the equation, we get -17.
f(x) = -(x - 4)^2 - 1
f(x) = -(-4)^2 - 1
f(x) = -16 - 1
f(x) = -17.

The x-intercept option is not true because the vertex is below the x axis and the negative coefficient gives the graph a downward trend. Therefore, there will be no x-intercept.

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3 years ago

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Answer:

Here's a quick sketch of how to calculate the distance from a point P=(x1,y1,z1)

(

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(

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and point Q=(x0,y0,z0)

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, which we could write as Ax+By+Cz+D=0

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3 years ago

Formulate the following problem as least squares problems. For each problem, give a matrixA and a vector b such that the problem

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Answer:

a) $A=\left[\begin{array}{ccc}1&2&3\\1&-1&1\end{array}\right]$

$b=\left[\begin{array}{ccc}0\\1\end{array}\right]$

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c) $A=\left[\begin{array}{ccc}0&6\sqrt{2} &0\\\sqrt{3} &3\sqrt{3} &0\\2&-16&0\end{array}\right]$

$x=\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]$

$b=\left[\begin{array}{ccc}-\sqrt{2} \\\sqrt{3} \\6\end{array}\right]$

Step-by-step explanation:

a) considering the equation:

Minimize $x_{1}^{2} +2x_{2}x^{2} +3x_{3}^{2}+(x_{1} -x_{2} +x_{3} -1)^{2} +(-x_{1} -4x_{2} +2)^{2}$

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vector b

$b=\left[\begin{array}{ccc}0\\1\end{array}\right]$

b) If Pxn is matrix B and p-vector d, we have:

minimize $(-6x_{2}+4)^{2} +(-4x_{1} +3x_{2} -1)+(x_{1} +8x_{2} -3)^{2}$

$Ax=\left[\begin{array}{ccc}0&-6&0\\-4&3&0\\1&8&0\end{array}\right]$

$\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]$

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in matrix:

$A=\left[\begin{array}{ccc}0&6\sqrt{2} &0\\\sqrt{3} &3\sqrt{3} &0\\2&-16&0\end{array}\right]$

$x=\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]$

$b=\left[\begin{array}{ccc}-\sqrt{2} \\\sqrt{3} \\6\end{array}\right]$

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3 years ago