Solve the system of equations. y = x^2 - 27x - 50 y = -27x + 50 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = x^2 - 27x - 50 y = -27x + 50 Set the two equations equal to each other to find the x-values where they intersect. x^2 - 27x - 50 = -27x + 50Simplify Quadratic Equation: Simplify the equation by adding 27x to both sides and adding 50 to both sides to get the quadratic equation in standard form. x^2 - 27x - 50 + 27x + 50 = -27x + 50 + 27x + 50 x^2 = 100Solve for x: Solve for x by taking the square root of both sides. sqrt(x^2) = sqrt(100) x = 10 or x = -10Find y-Values: Find the corresponding y-values by substituting x = 10 and x = -10 into the second equation y = -27x + 50. For x = 10: y = -27(10) + 50 = -270 + 50 = -220 For x = -10: y = -27(-10) + 50 = 270 + 50 = 320Write Coordinates: Write the coordinates in exact form. First Coordinate: (10, -220) Second Coordinate: (-10, 320)

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Solve the system of equations. $\newline$ $y = x^2 - 27x - 50$ $\newline$ $y = -27x + 50$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Algebra 2

Solve a system of linear and quadratic equations: parabolas

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Q. Solve the system of equations.

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y = x^2 - 27x - 50

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y = -27x + 50

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Write the coordinates in exact form. Simplify all fractions and radicals.

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(______,______)

\newline

(______,______)

Set Equations Equal: We have the system of equations: $\newline$ $y = x^2 - 27x - 50$ $\newline$ $y = -27x + 50$ $\newline$ Set the two equations equal to each other to find the $x$ -values where they intersect. $\newline$ $x^2 - 27x - 50 = -27x + 50$
Simplify Quadratic Equation: Simplify the equation by adding $27x$ to both sides and adding $50$ to both sides to get the quadratic equation in standard form. $\newline$ $x^2 - 27x - 50 + 27x + 50 = -27x + 50 + 27x + 50$ $\newline$ $x^2 = 100$
Solve for x: Solve for x by taking the square root of both sides. $\newline$ $\sqrt{x^2} = \sqrt{100}$ $\newline$ $x = 10$ or $x = -10$
Find y-Values: Find the corresponding y-values by substituting $x = 10$ and $x = -10$ into the second equation $y = -27x + 50$ . For $x = 10$ : $y = -27(10) + 50 = -270 + 50 = -220$ For $x = -10$ : $y = -27(-10) + 50 = 270 + 50 = 320$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(10, -220)$ $\newline$ Second Coordinate: $(-10, 320)$