F.4 MATH easy question>

y = -x^2 + 6x + a - 9

From the graph, it does not intercept with the x-axis

So, -x^2 + 6x + a - 9 = 0 has no real roots

Discriminant < 0

(6)^2 - 4(-1)(a - 9) < 0

36 + 4a - 36 < 0

a < 0


b. a < 0

So, a + 9 < 9

-(a + 9) > -9

Therefore, y = -x^2 + 6x - (a + 9)

We put y = 0,

-x^2 + 6x - (a + 9) = 0

Discriminant

= (6)^2 - 4(-1)[-(a + 9)]

= 36 - 4(a + 9)

> 36 - 4(9)

= 0

So, the discriminant > 0

The graph intersects the x-axis at 2 distinct points.