Answer:
-16
Step-by-step explanation:
-16... using d = b²-4ac
Answer:
A= 0.5 and B= 4040
Step-by-step explanation:
If you write out the equation and rearrange a little it gets easier to understand.
( a + b) + (a*b) + (a - b) you can rewrite this as
a + b + a - b + (a*b) this is the same as 2a + ab = 2021
The way I looked at it is to figure out how to get that number 1 at the end.
The number 2020 is easy to get to. How can you get the number 1 using either 2a or ab.
I looked at a = 0.5. 2 times 0.5 would be 1.
So now what would b have to be? We can get the 1 at the end with the 2a part of the equation so now we have to get ab = 2020.
b = 2020/a which using our a = 0.5, you can see that b would have to equal 4040. Test it all out in your equation.
0.5 + 4040 + (0.5 * 4040) + 0.5 - 4040
4040.5 + (2020) - 4039.5 = 2021
So A = 0.5 and B = 4040
Answer:
a) b = 8, c = 13
b) The equation of graph B is y = -x² + 3
Step-by-step explanation:
* Let us talk about the transformation
- If the function f(x) reflected across the x-axis, then the new function g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then the new function g(x) = f(-x)
- If the function f(x) translated horizontally to the right by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then the new function g(x) = f(x + h)
In the given question
∵ y = x² - 3
∵ The graph is translated 4 units to the left
→ That means substitute x by x + 4 as 4th rule above
∴ y = (x + 4)² - 3
→ Solve the bracket to put it in the form of y = ax² + bx + c
∵ (x + 4)² = (x + 4)(x + 4) = (x)(x) + (x)(4) + (4)(x) + (4)(4)
∴ (x + 4)² = x² + 4x + 4x + 16
→ Add the like terms
∴ (x + 4)² = x² + 8x + 16
→ Substitute it in the y above
∴ y = x² + 8x + 16 - 3
→ Add the like terms
∴ y = x² + 8x + 13
∴ b = 8 and c = 13
a) b = 8, c = 13
∵ The graph A is reflected in the x-axis
→ That means y will change to -y as 1st rule above
∴ -y = (x² - 3)
→ Multiply both sides by -1 to make y positive
∴ y = -(x² - 3)
→ Multiply the bracket by the negative sign
∴ y = -x² + 3
b) The equation of graph B is y = -x² + 3
