Answer:
1. x-intercepts are x=6 and x=-4 or (6,0) and (-4,0). the y-intercept is y=-24 or (0,-24)
2. x-intercepts are x=2 and x=-7 or (2,0) and (-7,0). the y-intercept is y=-42 or (0,-42)
3. The x intercepts are x=5 and x=-5 or (5,0) and (-5,0). the y-intercept is y=-25 or (0, -25)
Explanation:
for the first one, the given is y=x^2-2x-24
to factor we know that we need to find two numbers that multiply to be -24 and add to be -2
these numbers are -6 and +4
we now have y=(x-6)(x+4)
to find the intercepts we set these two values equal to zero
x-6=0 and x+4=0
we then add their inverse to get
x=6 and x=-4 as the x-intercepts
The y intercept is when x=0 so we just substitute 0 into the original equation and get y=-24
For the second one we start with y=3x^2+15x-42
To start, I factor out a 3 because 3 can go into each of the terms to get
y = 3(x^2+5x-14)
I then factor the expression in the parentheses to get
y= 3(x-2)(x+7)
we then set the parentheses equal to zero
x-2=0 and x+7=0
x=2 and x=-7
Then for the y-intercept we substitute zero in for x to get y=-42
For the third one we are given y=3x^2-75
I factored out a 3 to get
y=3(x^2-25)
looking at x^2-25, I see that 25 is a perfect square which means that this is a difference of squares problem.
This means that the second term is equal to the positive square root of 25 and the negative square root of 25
since the square root of 25 is 5 we now have
y=3(x+5)(x-5)
after setting it equal to zero we get x=5 and x=-5
For the y intercept we set x equal to zero and get y= -25