Question

Someone help me out really quick

Answer 1

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 = $\frac{-b}{2a}$ , 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 = $\frac{--20}{-2(2)}$ = $\frac{20}{-4}$

∴ 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)