Question

Graph y > x^2 - 5. Click on the graph until the correct one appears.

Answer 1

`y=x^2\\\\for\ x=\pm2\to y=(\pm2)^2=4\to(-2;\ 4);\ (2;\ 4)\\\\for\ x=\pm1\to y=(\pm1)^2=1\to (-1;\ 1);\ (1;\ 1)\\\\for\ x=0\to y=0^2=0\to (0;\ 0)`

Shift the graph of the function y = x², 5 units down /look at the picture #1/.

`y > x^2-5` /look at the picture #2/ - your answer

Answer 2

Graph 2

Explanation:

Here, the given inequality is,

`y>x^2-5-----(1)`

At (0,0),

`0>0-5`

`\implies 0 > -5` ( True )

So, The shaded region must contain the origin,

Hence, Graph 1 and Graph 3 can not be the graph of
`y>x^2-5`,

Now, we know that, The standard form of a parabola is,

`y=a(x-h)^2+k`

Where, (h,k) is the vertex of the parabola,

From equation (1), the related equation of inequality (1) can be written,

`y=(x-0)^2+(-5)`

By Comparing,

The vertex of the related parabola of inequality (1) is (0,-5),

⇒ The vertex of the given parabola must be lie on the negative y-axis

Thus, Graph 3 can not be the graph of the given equation,

Therefore, Graph 2 must be the graph of the given inequality.