Answer:
x is equal to 2.5 and -4.5
Step-by-step explanation:
-4(x + 1)² - 3 = -51
-4(x² + 2x + 1) - 3 = -51
-4x² - 8x -3 - 3 = -51
-4x² - 8x - 6 = -51
-4x² - 8x = -45
-4(x^2 + 2x) = -45
-4(x^2 + 2x + 1) = -49
-4(x + 1)² = -49
(x + 1)² = 49/4
x + 1 = ± √(49/4)
x + 1 = ± 7/2
x = -1 ± 3.5
x = 2.5, -4.5
STEP-BY-STEP SOLUTION:
Let's first establish the inequality which we need to solve as displayed below:
y + 1 < 3
To begin with, we need to make ( y ) the subject by keeping it on the left-hand side of the inequality and placing all other numbers on the right-hand side of the equality as displayed below:
y + 1 < 3
y < 3 - 1
Then, we simply simplify / solve as displayed below:
y < 3 - 1
y < 2
ANSWER:
y < 2
Answer:
g(x) = - x² - 4 ⇒ A
Step-by-step explanation:
Let us revise the reflection and translation of a function
- If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k
f(x) = x² is the blue curve
g(x) is its image is the red curve
∵ g(x) is the image of f(x)
∵ f(x) is opened upward
∵ g(x) is opened downward
→ That means the sign of y-coordinates of all points on the blue
graph are opposite
∴ f(x) is reflected about the x-axis
∴ Its image is - f(x)
∵ The vertex of f(x) is (0, 0)
∵ The vertex of g(x) = (0, -4)
→ That means the function translated 4 units down
∴ - f(x) is translated 4 units down
∴ Its image is - f(x) - 4
∴ g(x) = - f(x) - 4
∵ f(x) = x²
∴ g(x) = - x² - 4
