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3 years ago

7n2 + 5 = 453 Solve the quadratic function

Mathematics

2 answers:

Reptile [31]3 years ago

8 0

7n^2 + 5 = 453

Subtract 5 from both sides:

7n^2 = 448

Divide both sides by 7:

N^2 = 64

Take the square root of both sides:

N = 8

Olenka [21]3 years ago

6 0

See attachment for math work and answer.

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How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y

son4ous [18]

Solution:

Given:

$x^2=6y$

Part A:

The vertex of an up-down facing parabola of the form;

$\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}$

Rewriting the equation given;

$\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\ \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\ \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\ \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\ \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}$

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

$\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}$

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

$\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}$

Therefore, the focus is;

$(0,\frac{3}{2})$

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

$\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}$

Therefore, the directrix is;

$y=-\frac{3}{2}$

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1 year ago

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Ghella [55]

Answer:

$84s^{2} t\sqrt{35st}$

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3 years ago

Read 2 more answers

What is a quadratic equation? And how do you solve them?

Allisa [31]

Answer:

A quadratic equation is some thing like

(x+2)^2

(x+2)(x+5)

In order to solve them, the most basic method is the FOIL method

F-First

O-Outside

I-Inner

L-Last

So for example

(x+2)^2

Which is basically

(x+2)(x+2)

So the first is the 2 Xs

(x+2)(x+2)

x*x=x^2

The outer is the x and the 2,

(x+2)(x+2)

2*x=2x

Now the Inner which is the 2 and the x

(x+2)(x+2)

2*x=2x

And finally the last which is the 2 and the second 2

(x+2)(x+2)

2*2=4

Now add them all up

X^2+2x+2x+4

Combine like terms

x^2+4x+4

There you have it

Do the same with every other quadratic equation

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3 years ago

Answer asap, please<br> needed by 2:00 pm

myrzilka [38]

Answer:

x < -3

Step-by-step explanation:

The domain in which the function is increasing or getting bigger is from x is negative infinity to is -3

x < -3

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