Answer and Step-by-step explanation: <u>Standard</u> <u>form</u> of a quadratic equation is expressed as: y=ax²+bx+c, while <u>vertex</u> <u>form</u> is written as:
y=a(x-h)²+k.
The similarities between standard and vertex forms is that they show if the graph of the equation has a <u>minimum</u> (when a>0) or <u>maximum</u> (a<0) and it's easier to determine the y-intercept: for standard, the value of c is the intercept; for vertex, the value k is the intercept.
The advantage of standard form is that you can determine the product and sum of the equation's roots, which is a method to determine them.
The advantages of vertex form are: easier to find the vertex of the graph, which is the pair (h,k) and the axis of symmetry, which is the value of h.
Y = 2x + 5
If you take the height at 10 days, 25 centimeters, after 10 more days the height is 45 centimeters, meaning for those 10 extra days the been plant grown 20 centimeters. Since we're told the plant is growing at a constant rate, this shows the bean plant is growing 2 centimeters per day. We can represent this with y = 2x. (After 10 days, the bean plant will be 20 centimeters, after 20 days, the bean plant will be 40 centimeters, etc.)
However, this is not completely true yet. As you can see, after the first 10 days the plant is not 20 centimeter, it's 25 centimeters. We already know the rate in which the plant is changing, but now we need to find the height that the plant was originally, before it started growing.
After the first 10 days, the plant is 25 centimeters tall. Since we know that the plant is growing 2 centimeters per day, we can subtract 20 from 25 to find the original height of the bean plant.
25 - 20 = 5
The bean plant was originally 5 centimeters.
This makes our final equation y = 2x + 5.
2x is the slope, and 5 is the y intercept.
Hope this helps1!
==> I can't be sure of the equation. There's a blank space
between '5t' and '8', where an operation must be.
I think the operation is more likely ' + ' (addition). Brainly usually
does show the ' - ' if it's subtraction, but goes blank if it's addition.
Tell you what I'll do: Since you sound so desperate, and you're being
so generous with your points, I'll show you how to figure it out both ways.
----------------------------------------
If it's subtraction: 5t - 8 = 43
Add 8 to each side: 5t = 51
Divide each side by 5 : t = 51/5
t = 10 and 1/5
--------------------------------------------
If it's addition: 5t + 8 = 43
Subtract 8 from each side: 5t = 35
Divide each side by 5 : t = 7
if you're trying to solve for x, and it is equal to zero, then it would be -3. plug it in and it would all cancel out
