The function k(x) = -2x² + 8x + 13 algebraically
Step-by-step explanation:
h(x) = x² - 4x - 5
We need to find k(x) = -2h(x) + 3
1. Multiplied h(x) by -2 means stretched it vertically by scale factor 2
and then reflected it across the x-axis
2. Added 3 means translate it up 3 units
Let us find k(x) algebraically
∵ k(x) = -2h(x) + 3
∵ h(x) = x² - 4x - 5
∵ -2h(x) = -2(x² - 4x - 5)
∴ -2h(x) = -2(x²) + -2(-4x) + -2(-5)
∴ -2h(x) = -2x² + 8x + 10
- Substitute it in k(x)
∴ k(x) = -2x² + 8x + 10 + 3
- Add like terms
∴ k(x) = -2x² + 8x + 13
The function k(x) = -2x² + 8x + 13 algebraically
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