Solve the system of equations. y = -28x - 6 y = x^2 - 32x - 38 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal y. -28x - 6 = x^2 - 32x - 38Move Terms to One Side: Move all terms to one side to set the equation to zero. x^2 - 32x + 28x - 38 + 6 = 0 x^2 - 4x - 32 = 0Factor Quadratic Equation: Factor the quadratic equation. x^2 - 4x - 32 = (x - 8)(x + 4)Solve for x: Set each factor equal to zero and solve for x. (x - 8) = 0 or (x + 4) = 0 x = 8 or x = -4Substitute x to Find y: Substitute x back into one of the original equations to find y. For x = 8: y = -28(8) - 6 which is y = -224 - 6 so y = -230. For x = -4: y = -28(-4) - 6 which is y = 112 - 6 so y = 106.Write Coordinates: Write the coordinates in exact form. First Coordinate: (8, -230) Second Coordinate: (-4, 106)

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Solve the system of equations. $\newline$ $y = -28x - 6$ $\newline$ $y = x^2 - 32x - 38$ $\newline$ 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 = -28x - 6

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y = x^2 - 32x - 38

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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 since they both equal $y$ . $-28x - 6 = x^2 - 32x - 38$
Move Terms to One Side: Move all terms to one side to set the equation to zero. $\newline$ $x^2 - 32x + 28x - 38 + 6 = 0$ $\newline$ $x^2 - 4x - 32 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $x^2 - 4x - 32 = (x - 8)(x + 4)$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $(x - 8) = 0$ or $(x + 4) = 0$ $\newline$ $x = 8$ or $x = -4$
Substitute $x$ to Find $y$ : Substitute $x$ back into one of the original equations to find $y$ . For $x = 8$ : $y = -28(8) - 6$ which is $y = -224 - 6$ so $y = -230$ . For $x = -4$ : $y = -28(-4) - 6$ which is $y$ $0$ so $y$ $1$ .
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(8, -230)$ $\newline$ Second Coordinate: $(-4, 106)$