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3 years ago

Choose the equation below that represents the line passing through the point -3,-1 with the slope of four

Mathematics

1 answer:

tresset_1 [31]3 years ago

5 0

Answer:

y+1 = 4(x+3)

Step-by-step explanation:

To write the equation of a line use the point slope form by substituting m = 4 and the point (-3,-1).

$y - y_1 =m(x-x_1)\\y --1 = 4(x--3)\\y+1 = 4(x+3)$

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Read 2 more answers

Identify the vertex, the axis of symmetry, the maximum or minimum value, and the range of the parabola for y=x^2+6x+13

charle [14.2K]

Answer:

Step-by-step explanation:

First we can determine the x value of our vertex via the equation:

$x=\frac{-b}{2a}$

Note that in general a quadratic equation is such that:

$ax^2+bx+c$

In this case a,b and c are the coefficients and so a=1, b=6 and c=13.

Therefore we can determine the x component of the vertex by plugging in the values known and so:

$x=\frac{-b}{2a}=\frac{-6}{2(1)}=\frac{-6}{2}=-3$

Now we can determine the y-component of our vertex by plugging in the x-component to the equation and so:

$f(x)=x^2+6x+13\\\\f(-3)=(-3)^2+6(-3)+13\\\\f(-3)=4$

Therefore our vertex is (-3,4). Now in vertex our x component determines is the axis of symmetry so the equation for axis of symmetry is:

x=-3

Similarly, the y-component of our vertex is the minimum or maximum. In this case it is the minimum you can determine this because a is positive meaning that the parabola will point up, and so the equation for the minimum is:

y=4

The range of the formula is the smallest y-value meaning the minimum y=4 and all real numbers that are more than 4, mathematically:

Range = All real numbers greater than or equal to 4.

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3 years ago