Which of the following represents the function f(x) = x2 − 14x − 1 in vertex form? Identify the vertex.

Mathematics

1 answer:

RUDIKE [14]2 years ago

8 0

The vertex is (7,-50)
***rewrite in standard form***

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Solve by using substitution<br>-7x-2y=-13 and x-2y=11

netineya [11]

$\left \{ {{-7x-2y=-13} \atop {x-2y=11}} \right. \\\\ \left \{ {{-7x-2y=-13} \atop {x=11+2y}} \right.\\\\
Substitute\ second\ equation\ into\ the\ first\ one:\\\\
-7(11+2y)-2y=-13\\
-77-14y-2y=-13\\
-77-16y=-13\ \ \ |Add\ 77\\
-16y= 64\ \ \ |Divide\ by\ -16\\
y=-4\\\\x=11+2y=11+2*(-4)=11-8=3\\\\ \left \{ {{y=-4} \atop {x=3}} \right.$

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Step-by-step explanation:

A vertical line always has an undefined slope.

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Find the equation of the line that is parallel to the given line and passes through the given point

Sati [7]

Answer:

$\huge\boxed{y=-\dfrac{1}{4}x-1\to x+4y=-4}$

Step-by-step explanation:

$\text{Let}\ k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\l\ ||\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\==========================\\\\\text{We have}\ x+4y=-6.\\\text{Convert to the slope-intercept form:}\\\\x+4y=-6\qquad\text{subtract}\ x\ \text{from both sides}\\\\4y=-x-6\qquad\text{divide both sides by 4}\\\\y=\dfrac{-x}{4}-\dfrac{6}{4}\\\\y=-\dfrac{1}{4}x-\dfrac{3}{2}\to m_1=-\dfrac{1}{4}$

$\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (9,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}\\\\x=9,\ y=-3\\\\-3=-\dfrac{1}{4}(9)+b\\\\-3=-\dfrac{9}{4}+b\qquad\text{add}\ \dfrac{9}{4}\ \text{to both sides}\\\\-\dfrac{12}{4}+\dfrac{9}{4}=b\to b=-\dfrac{3}{4}$

$x=8,\ y=-3\\\\-3=-\dfrac{1}{4}(8)+b\\\\-3=-2+b\qquad\text{add 2 to both sides}\\\\-1=b\to b=-1$

$\text{Therefore the equation is:}\ y=-\dfrac{1}{4}x-1.\\\\\text{Convert to the standard form}\ Ax+By=C:\\\\y=-\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4y=-x-4\qquad\text{add}\ x\ \text{to both sides}\\\\x+4y=-4$

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3 years ago

Determine the zeros of f(x)=x^3+7x^2+10x-6

igor_vitrenko [27]

Hello,
x^3+7x^2+10x-6=x^3+3x^2+4x^2+12x-2x-6
=x²(x+3)+4x(x+3)-2(x+3)
=(x+3)(x²+4x-2)
=(x+3)(x+2-√7)(x+2+√7)

zeroes={-3,-2+√7,-2-√7}

4 0

2 years ago