Question

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

graph?

f(x) = 4 – x²


g(x) = ?


O A. g(x) = (7 - x)2
O B. g(x) = 1 - x2
O C. g(x) = 7 - x2
D. g(x) = (1 - x)2

Answer 1

Option B is correct .

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) }}`

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

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}}`

Hence option B is correct .

Answer 2

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

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!