A parabola is a quadratic function, and a quadratic can be expressed in vertex form, which is:
y=a(x-h)^2+k, where (h,k) is the vertex (absolute maximum or minimum point of the quadratic)
In this case we are given that (h,k) is (-5,80) so we have so far:
y=a(x--5)^2+80
y=a(x+5)^2+80, we are also told that it passes through the point (0,-45) so:
-45=a(0+5)^2+80
-45=25a+80 subtract 80 from both sides
-125=25a divide both sides by 25
-5=a, so now we know the complete vertex form is:
y=-5(x+5)^2+80
The x-intercepts occur when y=0 so:
0=-5(x+5)^2+80 add 5(x+5)^2 to both sides
5(x+5)^2=80 divide both sides by 5
(x+5)^2=16 take the square root of both sides
x+5=±√16 which is
x+5=±4 subtract 5 from both sides
x=-5±4 so the x-intercepts are:
x=-1 and -9
Answer:
1.no 2.no 3.no 4.no 5.yes 6.yes
7.yes 8.yes 9.no 10.yes 11. yes 12.yes
Step-by-step explanation:
hope that helps
Answer:
7.28011
Step-by-step explanation:
X1 =-3
X2 =-5
Y1 =8
Y2 =1
Distance Formula = √(X2-X1)²+ (Y2-y1)²
Step 1. calculate (X2-X1)²
(-5 - -3)2 = 4
Step 2. calculate (Y2-Y1)²
(1 - 8)2 = 49
Step 3. calculate √4 + 49
= 7.28011
First combine the like terms 3y + 2y to get 5y. Then combine 4 + 1 to get 5. Your equation will now be 80 = 5y + 5. To solve for y, 5 needs to be subtracted from both sides of the equation leaving 75 = 5y. Final step to solving for y, 5 needs to be divided from each side of the equation leaving the final answer of
15 = y.