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1 year ago

X2 - 4x + 4 = 0 solve following quadratic equations graphically and a table

1 answer:

6 0

Let's create a table, and use arbitrary values of x between -3 and 3 (if the solution is not in this interval, we can use another one later). If we call:

$f(x)=x^2-4x+4$

We want to find the x's for with f(x) = 0

This is the table:

And now we can evaluate f(x) in each value of x to complete the table:

$\begin{gathered} f(-3)=(-3)^2-4\cdot(-3)+4=9+12+4=25 \\ f(-2)=(-2)^2-4\cdot(-2)+4=4+8+4=16 \\ f(-1)=(-1)^2-4\cdot(-1)+4=1+4+4=9 \\ f(0)=0^2-4\cdot0+4=4 \\ f(1)=1^2-4\cdot1+4=1-4+4=1 \\ f(2)=2^2-4\cdot2+4=4-8+4=0 \\ f(3)=3^2-4\cdot3+4=9-12+4=1 \end{gathered}$

The table is:

If we use this values and plot them in the cartesian plane.

We get:

And now if we plot a line that connects the points, we get the graph of the quadratic equation:

Since the problem ask us to find the value of x for which f(x) = 0, we can see both in the table and in the graph that this value is x = 2

You might be interested in

Here are the ingredients for a cake. 0.225 kg butter 225 g sugar 225 g flour 0.2 kg eggs 250 g berries How much do the ingredien

viktelen [127]

Answer:

1125.

Step-by-step explanation:

I'm going to work out the answer is grams.

1kg = 1000g

0.225kg of butter = 225g, 225g of sugar, 225g of flour, 0.2kg of eggs = 200g, 250g of berries.

225 + 225 + 225 + 200 +250 = 1125.

Hope that helps. x

5 0

2 years ago

Read 2 more answers

AC = Round your answer to the nearest hundredth.

dusya [7]

Answer:

AC ≈ 5.03

Step-by-step explanation:

We can solve the problem above using the trigonometric ratio, they are;

SOH CAH TOA

sin Ф = opposite / hypotenuse

cosФ= adjacent/ hypotenuse

tan Ф = opposite / adjacent

From the diagram above, in reference to angle B;

opposite =AC and adjacent =BC

Since we have opposite and adjacent, the best formula to use is

tanФ = opposite / adjacent

tan B = AC / BC

tan 40 = AC/ 6

Multiply both-side of the equation by 6

6× tan 40 = AC/ 6 × 6

At the right-hand side of the equation, 6 will cancel-out 6 leaving us with just AC

6×tan 40 = AC

5.034598 = AC

AC ≈ 5.03 to the nearest hundredths

4 0

3 years ago

g Use this to find the equation of the tangent line to the parabola y = 2 x 2 − 7 x + 6 at the point ( 4 , 10 ) . The equation o

natali 33 [55]

Answer:

The tangent line to the given curve at the given point is $y=9x-26$ .

Step-by-step explanation:

To find the slope of the tangent line we to compute the derivative of $y=2x^2-7x+6$ and then evaluate it for $x=4$ .

$(y=2x^2-7x+6)'$ Differentiate the equation.

$(y)'=(2x^2-7x+6)'$ Differentiate both sides.

$y'=(2x^2)'-(7x)'+(6)'$ Sum/Difference rule applied: $(f(x)\pmg(x))'=f'(x)\pm g'(x)$

$y'=2(x^2)'-7(x)'+(6)'$ Constant multiple rule applied: $(cf)'=c(f)'$

$y'2(2x)-7(1)+(6)'$ Applied power rule: $(x^n)'=nx^{n-1}$

$y'=4x-7+0$ Simplifying and apply constant rule: $(c)'=0$

$y'=4x-7$ Simplify.

Evaluate y' for x=4:

$y'=4(4)-7$

$y'=16-7$

$y'=9$ is the slope of the tangent line.

Point slope form of a line is:

$y-y_1=m(x-x_1)$

where $m$ is the slope and $(x_1,y_1)$ is a point on the line.

Insert 9 for $m$ and (4,10) for $(x_1,y_1)$ :

$y-10=9(x-4)$

The intended form is $y=mx+b$ which means we are going need to distribute and solve for $y$ .

Distribute:

$y-10=9x-36$

Add 10 on both sides:

$y=9x-26$

The tangent line to the given curve at the given point is $y=9x-26$ .

------------Formal Definition of Derivative----------------

The following limit will give us the derivative of the function $f(x)=2x^2-7x+6$ at $x=4$ (the slope of the tangent line at $x=4$ ):

$\lim_{x \rightarrow 4}\frac{f(x)-f(4)}{x-4}$

$\lim_{x \rightarrow 4}\frac{2x^2-7x+6-10}{x-4}$ We are given f(4)=10.

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

Let's see if we can factor the top so we can cancel a pair of common factors from top and bottom to get rid of the x-4 on bottom:

$2x^2-7x-4=(x-4)(2x+1)$

Let's check this with FOIL:

First: $x(2x)=2x^2$

Outer: $x(1)=x$

Inner: $(-4)(2x)=-8x$

Last: $-4(1)=-4$

---------------------------------Add!

$2x^2-7x-4$

So the numerator and the denominator do contain a common factor.

This means we have this so far in the simplifying of the above limit:

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

$\lim_{x \rightarrow 4}\frac{(x-4)(2x+1)}{x-4}$

$\lim_{x \rightarrow 4}(2x+1)$

Now we get to replace x with 4 since we have no division by 0 to worry about:

2(4)+1=8+1=9.

6 0

3 years ago

Find the slope-intercept equation of the line that passes through (0, 2) and has a slope of 1/2

julia-pushkina [17]

Answer:

1/2

Step-by-step explanation:

4 0

3 years ago

Which function has lowest rate of change?

Delvig [45]

Answer:

A: Algebraic Function

Step-by-step explanation:

Algebraic function is given as;

5x – 2y = 15

Since we are dealing with rate of change, let's make y the subject first and find dy/dx.

Thus;

2y = 5x - 15

y = (5x/2) - 15/2

dy/dx = 5/2

dy/dx = 2.5

The verbal function is given as;

Cost of 5 pencils is 15 dollars

Thus, rate of 1 pencil = 15/5 = 3 pencils per dollar

We can see that the lowest rate of change is 2.5 and it is the algebraic function.

8 0

3 years ago