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Bond [772]
3 years ago
13

The graphs below have the same shape. What is the equation of the red

Mathematics
2 answers:
anyanavicka [17]3 years ago
8 0

Answer:

Option B is correct .

Step-by-step explanation:

According to Question , both the graph have same shape . If we look at the the first graph it cuts x - axis at (0 , 2) and ( 0 , -2) . Hence x = 2 and -2 are the zeroes of the equation .

And ,the given function is ,

\implies f(x) = 4 - x^2 \\\\\implies f(x) = 4-x^2=0 \\\\\implies 2^2-x^2=0\\\\\implies (2-x)(2+x) = 0 \\\\\boxed{\red{\bf \implies x = 2 , (-2) }}

<u>Hence ,we can can see that x = </u><u> </u><u>2</u><u> </u><u>and</u><u> </u><u>(</u><u>-</u><u>2</u><u>)</u><u> </u><u>are</u><u> </u><u>the</u><u> </u><u>zeroes </u><u>of </u><u>graph</u><u>. </u><u> </u>

This implies that if we know the zeroes , we can frame the Equation.

On looking at second parabola , it's clear that cuts x - axis at ( 1, 0 ) and (-1,0). So , 1 and -1 are the zeroes of the quadratic equation . Let the function be g(x) . Here , a and ß are the zeroes.

\implies g(x) = (x-\alpha)(x-\beta) \\\\\implies g(x) = (1+x)(1-x) \\\\\boxed{\pink{\bf \implies g(x) = 1 - x^2}}

<u>Hence </u><u>option </u><u>B</u><u> </u><u>is</u><u> </u><u>corre</u><u>ct</u><u> </u><u>.</u>

umka2103 [35]3 years ago
3 0

Answer:

O B. g(x) = 1 - x^2

Step-by-step explanation:

Since the function in the graph is headed downwards, we know the portion of x^{2} is negative. And since the highest point of the red line on the y-axis is 1, we can conclude the function represented by the red line is 1 - x^2.

Hope this helped!

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