Simplify the expression

Mathematics

1 answer:

erastova [34]3 years ago

6 0

Answer : A

We need to simplify the given expression

Lets factor numerator first

$2x^2-5x-3$ =(2x+1)(x-3)

$x^2+8x+15$ =(x+5)(x+3)

Now we factor the denominator

$x^2+x-20$ =(x+5)(x-4)

$2x^2+9x+4$ =(2x+1)(x-4)

Now we simplify it

$\frac{(2x+1)(x-3)}{(x+5)(x-4)} * \frac{(x+5)(x+3)}{(2x+1)(x-4)}$

Now cancel out same factors. so we left with

$\frac{(x+3)(x-3)}{(x+4)(x-4)} }$

Now multiply the factors

$\frac{x^2-9}{x^2-16} }$

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Use the parabola tool to graph the quadratic function f(x)=−12x2+7. Graph the parabola by first plotting its vertex and then plo

Fudgin [204]

First we find the vertex of parabola $f(x)=-12 x^{2} +7$

The vertex of parabola is $( \frac{-b}{2a},f( \frac{-b}{2a}))$
Here,
b = coefficient of x term
a = coefficient of x² term

For given parabola, b = 0 , a = -12

So,
$\frac{-b}{2a}= \frac{0}{-24} =0$

And,

$f( \frac{-b}{2a} )=f(0) = -12(0)+7=7$

Thus the vertex of parabola is (0, 7)

To find another point on parabola, substitute x by 1.

$f(1)=-12( 1^{2}) +7=-12+7=-5$

So the second point on parabola is (1,-5)

The plot of parabola is shown in image below: