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2 years ago

What is the product of (x − 3) and (x + 7)?

Mathematics

2 answers:

lidiya [134]2 years ago

5 0

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$\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond$

What is the product of (x-3) and (x+7)?

$\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\diamond$

First multiply the x's:-

x•x=x²

Now multiply x times 7:-

So we have

x²+7x

Now multiply -3 times x:-

-3x

So we have

x²+7x-3x

Now multiply 7 and -3:-

x²+7x-3x-21

On simplification,

x²+4x-21

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Alisiya [41]2 years ago

5 0

X times X +(-3) times X + X times 7 +(-3) times (7)=x^2 -3x +7x -21
= x ^2 +4x-21

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First, we are going to find the vertex of our quadratic. Remember that to find the vertex $(h,k)$ of a quadratic equation of the form $y=a x^{2} +bx+c$ , we use the vertex formula $h= \frac{-b}{2a}$ , and then, we evaluate our equation at $h$ to find $k$ .

We now from our quadratic that $a=2$ and $b=-32$ , so lets use our formula:
$h= \frac{-b}{2a}$
$h= \frac{-(-32)}{2(2)}$
$h= \frac{32}{4}$
$h=8$
Now we can evaluate our quadratic at 8 to find $k$ :
$k=2(8)^2-32(8)+56$
$k=2(64)-256+56$
$k=128-200$
$k=-72$
So the vertex of our function is (8,-72)

Next, we are going to use the vertex to rewrite our quadratic equation:
$y=a(x-h)^2+k$
$y=2(x-8)^2+(-72)$
$y=2(x-8)^2-72$
The x-coordinate of the minimum will be the x-coordinate of the vertex; in other words: 8.

We can conclude that:
The rewritten equation is $y=2(x-8)^2-72$
The x-coordinate of the minimum is 8