Linear and quadratic graphs

1. Suppose a linear grapg y = ax+b has both the x-intercept and y-intercept positive. What are the signs of a and b respectively?

y = ax+b
when x = 0, y = b >0 (y-intercept positive)
when y = 0,
0 = ax+b
x = -b/a >0 (x-intercept positive)
b/a<0 (negative)
as b is positive, a must be negative

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2.Suppose a quadratic graph has positive y-intercept and 2 distinct roots. Can you determine whether the graph opens upwards or downwards?

maybe i use 2 examples here

y = x^2 - 6x + 8
2 & 4 are the roots for y = 0
and the y-int is 8 (+ve)
==>the curve is downwards

y = -x^2 + 3x + 10
-2 & 5 are the roots for y = 0
and the y-int is 10 (+ve)
==>the curve is upwards

so we can not determind whether the curve is upwards or downwards

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3.Suppose a quadratic graph has both the y-intercept and y-coordinate of the vertex positive. Can you determine whether the graph opens upwards or downwards?

again i use 2 examples here

y = x^2 - 6x + 10
y = (x-3)^2 + 1
and the y-int is 10 (+ve)
the y-coordinate of the vertex = 1 (+ve)
==>the curve is downwards

y = -x^2 + 4x + 5
y = -(x-2)^2 +9
and the y-int is 5 (+ve)
the y-coordinate of the vertex = 5 (+ve)
==>the curve is upwards

so we can not determind whether the curve is upwards or downwards

1. Suppose a linear grapg y = ax+b has both the x-intercept and y-intercept positive. What are the signs of a and b respectively?
let x=0
then y=b
since y positive, b should be positive
let y=0
then
ax+b=0
since b and x positive, a should be negative
2.Suppose a quadratic graph has positive y-intercept and 2 distinct roots. Can you determine whether the graph opens upwards or downwards?
it should be open downwards
3.Suppose a quadratic graph has both the y-intercept and y-coordinate of the vertex positive. Can you determine whether the graph opens upwards or downwards?
we cannot determine whether the graph opens upwards or downwards
both situation may be occured