Question

Please show me how to solve this.

Answer 1

A = (0,4)

B = (5,9)

Explanation:

y=-x²+6x+4

So c=4

=> A = (0,4)

find the equation of the straight line with the 2 points you have:

(0,4) and (2,6)

put them in y=ax+b and find a & b

`4 = a * 0 + b = \\ 6 = a * 2 + b`

So b=4 & a=1 => y=x+4

Put the equation of line and parabola equal:

`y = x + 4 \\ y = - {x}^(2) + 6x + 4 \\ \\ x + 4 = - {x}^(2) + 6x + 4 \\ {x}^(2) - 5x = 0 \\ x(x - 5) = 0`

So x=0 or x=5

We know x=0 is where A located on

so B is located on x=5

y=x+4

put x=5

y=9

Finally:

A = (0,4)

B = (5,9)