No spam pls for which x is f(x)=-3 1. -7 2.-4 3. 4 4. 5

Mathematics

1 answer:

Ugo [173]3 years ago

5 0

9514 1404 393

Answer:

(a) -7

Step-by-step explanation:

You are given f(x) = -3. Look for -3 in the f(x) column. (You will find it in the <em>first row</em>.)

You want the corresponding value of x. It will be in the <em>first row</em> of the x column. The value there is -7.

The value of x for f(x) = -3 is -7.

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Write the quadratic function in the form g(x)=a (x-h)2 +kThen, give the vertex of its graph. G(x) =2x2 +20x+49Writing in the for

Snezhnost [94]

The quadratic function given to us is:

$g(x)=2x^2+20x+49$

We are asked to find the vertex form of the function.

The general formula for the vertex form of a quadratic equation is:

$\begin{gathered} g(x)=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the coordinate of the vertex} \end{gathered}$

In order to write the function in its vertex form, we need to perform a couple of operations on the function.

1. Add and subtract the square of the half of the coefficient of x to the function.

2. Factor out the function with its repeated roots and re-write the equation.

Now, let us solve.

1. Add and subtract the square of the half of the coefficient of x to the function.

$\begin{gathered} g(x)=2x^2+20x+49=2(x^2+10x+\frac{49}{2}) \\ \text{half of coefficient of x:} \\ \frac{10}{2}=5 \\ \text{square of the half of the coefficient of x:} \\ 5^2=25 \\ \\ \therefore g(x)=2(x^2+10x+25-25+\frac{49}{2}) \end{gathered}$

2. Factor out the function with its repeated roots and re-write the equation.

$\begin{gathered} g(x)=2(x^2+10x+25)-2(25+\frac{49}{2}) \\ re-\text{write the above function} \\ g(x)=2(x^2+10x+25)-1 \\ \text{Let us factorize this:} \\ g(x)=2(x+5)^2-1 \end{gathered}$

Therefore, we can conclude that the Equation and vertex of the equation is: