A
because c and g are same and g and e are complementary.
If P is a point in the x axis therefore this means that
the y must be zero. Hence the coordinate of p is (x, 0).
We can use the distance formula to solve for the value of
x:
d^2 = (x – x1)^2 + (y – y1)^2
13^2 = (x + 3)^2 + (0 – 5)^2
169 = (x + 3)^2 + 25
(x + 3)^2 = 144
x + 3 = ± 12
x = -15, 9
Hence P has two possible coordinates:
<span>(-15, 0) and (9, 0)</span>
Year 1 5000 X 1.03 5150
Year 2 5150 X 1.03 5305
Year 3 5305 X 1.03 5464
Year 4 5464 X 1.03 5628
Year 5 5628 X 1.03 5796
Year 6 5796 X 1.03 5970
Year 7 5970 X 1.03 6149
Year 8 6149 X 1.03 6334
Year 9 6334 X 1.03 6524
Year 10 6524 X 1.03 6720
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
