Solve the system of equations. y = 2x^2 - 38x + 7 y = -38x + 25 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: Set the two equations equal to each other to find the x-values where they intersect. y = 2x^2 - 38x + 7 y = -38x + 25 2x^2 - 38x + 7 = -38x + 25Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. 2x^2 - 38x + 7 + 38x - 25 = 0 2x^2 - 18 = 0Solve for x: Solve the quadratic equation for x. 2x^2 = 18 x^2 = 9 x = ±3Find Corresponding y-Values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. Let's use y = -38x + 25. For x = 3: y = -38(3) + 25 y = -114 + 25 y = -89 For x = -3: y = -38(-3) + 25 y = 114 + 25 y = 139Write Coordinates: Write the coordinates in exact form. First Coordinate: (3, -89) Second Coordinate: (-3, 139)

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Solve the system of equations. $\newline$ $y = 2x^2 - 38x + 7$ $\newline$ $y = -38x + 25$ $\newline$ 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.

\newline

y = 2x^2 - 38x + 7

\newline

y = -38x + 25

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: Set the two equations equal to each other to find the $x$ -values where they intersect. $\newline$ $y = 2x^2 - 38x + 7$ $\newline$ $y = -38x + 25$ $\newline$ $2x^2 - 38x + 7 = -38x + 25$
Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. $\newline$ $2x^2 - 38x + 7 + 38x - 25 = 0$ $\newline$ $2x^2 - 18 = 0$
Solve for x: Solve the quadratic equation for x. $\newline$ $2x^2 = 18$ $\newline$ $x^2 = 9$ $\newline$ $x = \pm3$
Find Corresponding y-Values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. Let's use $y = -38x + 25$ . For $x = 3$ : $y = -38(3) + 25$ $y = -114 + 25$ $y = -89$ For $x = -3$ : $y = -38(-3) + 25$ $y = 114 + 25$ $y = 139$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(3, -89)$ $\newline$ Second Coordinate: $(-3, 139)$