Solve the system of equations. y = x^2 - 12x - 9 y = -24x - 44 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = x^2 - 12x - 9 y = -24x - 44 To find the intersection points, we need to set the two equations equal to each other. x^2 - 12x - 9 = -24x - 44Rearrange and Solve: Now, we rearrange the equation to bring all terms to one side and set it equal to zero. x^2 - 12x - 9 + 24x + 44 = 0 x^2 + 12x + 35 = 0Factor Quadratic Equation: Next, we factor the quadratic equation. In the form ax^2 + bx + c, we need two numbers that multiply to c (35) and add up to b (12). These numbers are 5 and 7. (x + 5)(x + 7) = 0Solve for x: Now, we solve for x by setting each factor equal to zero. (x + 5) = 0 or (x + 7) = 0 This gives us x = -5 and x = -7.Find y Values: We have two values for x: x1 = -5 and x2 = -7. Now we need to find the corresponding y values by substituting x back into one of the original equations. We can use y = -24x - 44. For x1 = -5: y = -24(-5) - 44 = 120 - 44 = 76 For x2 = -7: y = -24(-7) - 44 = 168 - 44 = 124Coordinates of Intersection Points: We now have the coordinates of the intersection points in exact form. First Coordinate: (-5, 76) Second Coordinate: (-7, 124)

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Solve the system of equations. $\newline$ $y = x^2 - 12x - 9$ $\newline$ $y = -24x - 44$ $\newline$ 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 = x^2 - 12x - 9

\newline

y = -24x - 44

\newline

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the system of equations: $\newline$ $y = x^2 - 12x - 9$ $\newline$ $y = -24x - 44$ $\newline$ To find the intersection points, we need to set the two equations equal to each other. $\newline$ $x^2 - 12x - 9 = -24x - 44$
Rearrange and Solve: Now, we rearrange the equation to bring all terms to one side and set it equal to zero. $\newline$ $x^2 - 12x - 9 + 24x + 44 = 0$ $\newline$ $x^2 + 12x + 35 = 0$
Factor Quadratic Equation: Next, we factor the quadratic equation. $\newline$ In the form $ax^2 + bx + c$ , we need two numbers that multiply to $c$ ( $35$ ) and add up to $b$ ( $12$ ). These numbers are $5$ and $7$ . $\newline$ $(x + 5)(x + 7) = 0$
Solve for x: Now, we solve for $x$ by setting each factor equal to zero. $(x + 5) = 0$ or $(x + 7) = 0$ This gives us $x = -5$ and $x = -7$ .
Find y Values: We have two values for x: $x_1 = -5$ and $x_2 = -7$ . Now we need to find the corresponding y values by substituting x back into one of the original equations. We can use $y = -24x - 44$ . For $x_1 = -5$ : $y = -24(-5) - 44 = 120 - 44 = 76$ For $x_2 = -7$ : $y = -24(-7) - 44 = 168 - 44 = 124$
Coordinates of Intersection Points: We now have the coordinates of the intersection points in exact form. $\newline$ First Coordinate: $(-5, 76)$ $\newline$ Second Coordinate: $(-7, 124)$