The general equation of a parabola is y=ax^2+bx+c At the y-intercept, x=0 and y= -8: -8 = a(0)^2 + b(0) + c. Thus, c = -8. So, our equation becomes
y = ax^2 + bx - 8. Next, substitute -1.5 for x and -12.5 for y. Then,
-12.5 = a(-1.5)^2 + b(-1.5) - 8. This simplifies to -4.5 = a(2.25) - 1.5b.
Next, take advantage of the info that the vertex is at x= -1.5.
The formula for the vertex is x=-b/(2a). Letting this formula = -1.5,
-1.5 = -b/(2a). We can then solve for b: 1.5 = b/(2a), or 3a = b.
Now go back to the equation we derived previously: -4.5 = a(2.25) - 1.5b.
Substitute 3a for b:
-4.5 = a(2.25) - 1.5(3a). Then -4.5 = -2.25a, and a = 4.5/2.25 = 2.
Last, substitute a = 2 into 3a=b to determine the value of b.
b=3(2) = 6.
Therefore, your equation is y=2x^2 + 6x - 8.
Check this result. Substitute the coordinates of the vertex (-1.5,-12.5) into this equation. Is the equation still true? If so, your equation correctly represents this parabola.
is continuous over its domain, all real
.
Meanwhile,
is defined for real
.
If
, then we have
as the domain of
.
We know that if
and
are continuous functions, then so is the composite function
.
Both
and
are continuous on their domains (excluding the endpoints in the case of
), which means
is continuous over
.
Answer:
2ab(a + 3b)
Step-by-step explanation:
2a²b + 6ab²
Factor out 2ab
2ab(a + 3b)
Answer:
159.75
Step-by-step explanation:
23.50×5=117.5
117.5+42.25=159.75
