Solve the system of equations. y = -48x + 96 y = x^2 - 48x - 48 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. -48x + 96 = x^2 - 48x - 48Move Terms, Set to Zero: Move all terms to one side to set the equation to zero. 0 = x^2 - 48x + 48x - 48 - 96Simplify Equation: Simplify the equation by combining like terms. 0 = x^2 - 144Factor Quadratic: Factor the quadratic equation. 0 = (x - 12)(x + 12)Solve for x: Set each factor equal to zero and solve for x. x - 12 = 0 or x + 12 = 0 x = 12 or x = -12Substitute x, Find y: Substitute x = 12 into one of the original equations to find y. y = -48(12) + 96 y = -576 + 96 y = -480Write Coordinates: Substitute x = -12 into the same original equation to find y. y = -48(-12) + 96 y = 576 + 96 y = 672Write the coordinates in exact form. First Coordinate: (12, -480) Second Coordinate: (-12, 672)

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Solve the system of equations. $\newline$ $y = -48x + 96$ $\newline$ $y = x^2 - 48x - 48$ $\newline$ $\newline$ 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 = -48x + 96

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y = x^2 - 48x - 48

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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 $y$ . $-48x + 96 = x^2 - 48x - 48$
Move Terms, Set to Zero: Move all terms to one side to set the equation to zero. $\newline$ $0 = x^2 - 48x + 48x - 48 - 96$
Simplify Equation: Simplify the equation by combining like terms. $\newline$ $0 = x^2 - 144$
Factor Quadratic: Factor the quadratic equation. $\newline$ $0 = (x - 12)(x + 12)$
Solve for $x$ : Set each factor equal to zero and solve for $x$ .
$x - 12 = 0$ or $x + 12 = 0$
$x = 12$ or $x = -12$
Substitute $x$ , Find $y$ : Substitute $x = 12$ into one of the original equations to find $y$ . $y = -48(12) + 96$ $y = -576 + 96$ $y = -480$
Write Coordinates: Substitute $x = -12$ into the same original equation to find $y$ . $y = -48(-12) + 96$ $y = 576 + 96$ $y = 672$
Write Coordinates: Substitute $x = -12$ into the same original equation to find $y$ . $y = -48(-12) + 96$ $y = 576 + 96$ $y = 672$ Write the coordinates in exact form. $\text{First Coordinate: } (12, -480)$ $\text{Second Coordinate: } (-12, 672)$