Solve the system of equations. y = 3x^2 - 36x - 21 y = -36x - 18 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 the graphs intersect. y = 3x^2 - 36x - 21 y = -36x - 18 3x^2 - 36x - 21 = -36x - 18Simplify Equation: Simplify the equation by adding 36x and 21 to both sides. 3x^2 - 36x - 21 + 36x + 21 = -36x - 18 + 36x + 21 3x^2 = 3Isolate x^2: Divide both sides by 3 to isolate x^2. 3x^2 / 3 = 3 / 3 x^2 = 1Solve for x: Take the square root of both sides to solve for x. sqrt(x^2) = sqrt(1) x = 1 or x = -1Find y-values: Substitute the x-values back into one of the original equations to find the corresponding y-values. For x = 1: y = -36x - 18 y = -36(1) - 18 y = -36 - 18 y = -54Substitute x-values: Substitute the second x-value into the same equation. For x = -1: y = -36x - 18 y = -36(-1) - 18 y = 36 - 18 y = 18Write Coordinates: Write the coordinates in exact form. First Coordinate: (1, -54) Second Coordinate: (-1, 18)

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Solve the system of equations. $\newline$ $y = 3x^2 - 36x - 21$ $\newline$ $y = -36x - 18$ $\newline$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,) $\newline$

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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 = 3x^2 - 36x - 21

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y = -36x - 18

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

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(______,______)

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(______,______)

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Set Equations Equal: Set the two equations equal to each other to find the $x$ -values where the graphs intersect. $\newline$ $y = 3x^2 - 36x - 21$ $\newline$ $y = -36x - 18$ $\newline$ $3x^2 - 36x - 21 = -36x - 18$
Simplify Equation: Simplify the equation by adding $36x$ and $21$ to both sides. $\newline$ $3x^2 - 36x - 21 + 36x + 21 = -36x - 18 + 36x + 21$ $\newline$ $3x^2 = 3$
Isolate $x^2$ : Divide both sides by $3$ to isolate $x^2$ . $\newline$ $\frac{3x^2}{3} = \frac{3}{3}$ $\newline$ $x^2 = 1$
Solve for x: Take the square root of both sides to solve for x. $\newline$ $\sqrt{x^2} = \sqrt{1}$ $\newline$ $x = 1$ or $x = -1$
Find y-values: Substitute the x-values back into one of the original equations to find the corresponding y-values. $\newline$ For $x = 1$ : $\newline$ $y = -36x - 18$ $\newline$ $y = -36(1) - 18$ $\newline$ $y = -36 - 18$ $\newline$ $y = -54$
Substitute x-values: Substitute the second x-value into the same equation. $\newline$ For $x = -1$ : $\newline$ $y = -36x - 18$ $\newline$ $y = -36(-1) - 18$ $\newline$ $y = 36 - 18$ $\newline$ $y = 18$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(1, -54)$ $\newline$ Second Coordinate: $(-1, 18)$