How many solutions exist for the given equation?
1 answer:
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Answer:
Roots: 3.746 and -13.746
Vertex: (-5, 153)
Step-by-step explanation:
- The roots of the quadratic equation y = ax² + bx + c, are the values of x at y = 0
- Its vertex is (h, k), where, h =
, and k is the value of y at x = h
Let us use these facts to solve the question
∵ y = -2x² - 20x + 103
→ Compare it by the form of the equation above
∴ a = -2, b = -20, and c = 103
→ To find its roots equate y by 0
∵ 0 = -2x² - 20x + 103
→ Use your calculator to find the values of x
∴ x = 3.746427842 and x = -13.74642784
→ Round them to 3 decimal places
∴ x = 3.746 and x = -13.746
∴ Roots: 3.746 and -13.746
→ To find its vertex use the rule of h above
∵ a = -2 and b = -20
∵ h = =
∴ h = -5
→ To find k substitute y by k and x by -10 in the equation
∵ k = -2(-5)² - 20(-5) + 103
∴ k = -2(25) + 100 + 103
∴ k = -50 + 100 + 103
∴ k = 153
∴ The vertex of the quadratic is (-5, 153)
∴ Vertex: (-5, 153)
