Solve the system of equations. y = 9x^2 - 15x - 33 y = -15x + 3 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. 9x^2 - 15x - 33 = -15x + 3Move Terms to One Side: Move all terms to one side to set the equation to zero. 9x^2 - 15x - 33 + 15x - 3 = 0 9x^2 - 36 = 0Factor Quadratic Equation: Factor the quadratic equation. 9(x^2 - 4) = 0 9(x - 2)(x + 2) = 0Solve for x: Set each factor equal to zero and solve for x. x - 2 = 0 or x + 2 = 0 x = 2 or x = -2Substitute x Values: Substitute x values into the second equation to find y values. For x = 2: y = -15(2) + 3 = -30 + 3 = -27 For x = -2: y = -15(-2) + 3 = 30 + 3 = 33Write Coordinates: Write the coordinates in exact form. First Coordinate: (2, -27) Second Coordinate: (-2, 33)

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Solve the system of equations. $\newline$ $y = 9x^2 - 15x - 33$ $\newline$ $y = -15x + 3$ $\newline$ 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 = 9x^2 - 15x - 33

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y = -15x + 3

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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 $y$ . $9x^2 - 15x - 33 = -15x + 3$
Move Terms to One Side: Move all terms to one side to set the equation to zero. $\newline$ $9x^2 - 15x - 33 + 15x - 3 = 0$ $\newline$ $9x^2 - 36 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $9(x^2 - 4) = 0$ $\newline$ $9(x - 2)(x + 2) = 0$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $x - 2 = 0$ or $x + 2 = 0$ $\newline$ $x = 2$ or $x = -2$
Substitute x Values: Substitute $x$ values into the second equation to find $y$ values. $\newline$ For $x = 2$ : $y = -15(2) + 3 = -30 + 3 = -27$ $\newline$ For $x = -2$ : $y = -15(-2) + 3 = 30 + 3 = 33$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(2, -27)$ $\newline$ Second Coordinate: $(-2, 33)$