Question

F(x)=-2x²+8 and g(x)=1.75x+6, the y-axis and the line x=2.

Answer 1

The points of intersection between the graphs of
`\(f(x)=-2x^2+8\)` and
`\(g(x)=1.75x+6\)` with the y-axis and the line
`\(x=2\)` are (-2, 0) and (2, 0), respectively.

Step-by-step explanation:

To find the points of intersection, we set the two functions equal to each other and solve for
`\(x\)`:

`\[ -2x^2 + 8 = 1.75x + 6 \]`

Bringing all terms to one side, we get a quadratic equation:

`\[ -2x^2 - 1.75x + 2 = 0 \]`

Now, we can solve this quadratic equation for
`\(x\)`. The solutions will give us the x-coordinates of the points of intersection. Using the quadratic formula
`\(x = (-b \pm √(b^2-4ac))/(2a)\)`, where a = -2, b = -1.75, and c = 2, we find two solutions: x = -2 and x = 1.

Now that we have the x-coordinates, we can find the corresponding y-coordinates by plugging these values into either
`\(f(x)\)` or
`\(g(x)\)`. For x = -2,
`(f(-2) = -2(-2)^2 + 8 = 0\)`), and for x = 1, (g(1) = 1.75(1) + 6 = 7.75).

Therefore, the points of intersection are (-2, 0) and (2, 0), as these are the points where the graphs of
`\(f(x)\)` and
`\(g(x)\)` intersect the y-axis and the line x=2, respectively.