Solve the system of equations. y = x^2 - 20x + 37 y = -34x - 11 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = x^2 - 20x + 37 y = -34x - 11 Set the two equations equal to each other to find the x-values where they intersect. x^2 - 20x + 37 = -34x - 11Rearrange to Standard Form: Rearrange the equation to get a standard form quadratic equation. x^2 - 20x + 37 + 34x + 11 = 0 x^2 + 14x + 48 = 0Factor Quadratic Equation: Factor the quadratic equation. In quadratic equation ax^2 + bx + c, the factors are of the form (x + m)(x + n), where b is the sum and c is the product of m and n respectively. x^2 + 14x + 48 = 0 (x + 6)(x + 8) = 0Solve for x: Solve for x. Set each factor equal to zero and solve for x. (x + 6) = 0 or (x + 8) = 0 x = -6 or x = -8Find Corresponding y-Values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. We can use y = -34x - 11. For x = -6: y = -34(-6) - 11 y = 204 - 11 y = 193Find y-Value: Find the y-value for x = -8: y = -34(-8) - 11 y = 272 - 11 y = 261Write Coordinates: Write the coordinates in exact form. First Coordinate: (-6, 193) Second Coordinate: (-8, 261)

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Solve the system of equations. $\newline$ $y = x^2 - 20x + 37$ $\newline$ $y = -34x - 11$ $\newline$ 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 - 20x + 37

\newline

y = -34x - 11

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the system of equations: $\newline$ $y = x^2 - 20x + 37$ $\newline$ $y = -34x - 11$ $\newline$ Set the two equations equal to each other to find the $x$ -values where they intersect. $\newline$ $x^2 - 20x + 37 = -34x - 11$
Rearrange to Standard Form: Rearrange the equation to get a standard form quadratic equation. $\newline$ $x^2 - 20x + 37 + 34x + 11 = 0$ $\newline$ $x^2 + 14x + 48 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ In quadratic equation $ax^2 + bx + c$ , the factors are of the form $(x + m)(x + n)$ , where $b$ is the sum and $c$ is the product of $m$ and $n$ respectively. $\newline$ $x^2 + 14x + 48 = 0$ $\newline$ $(x + 6)(x + 8) = 0$
Solve for x: Solve for x. $\newline$ Set each factor equal to zero and solve for x. $\newline$ $(x + 6) = 0$ or $(x + 8) = 0$ $\newline$ $x = -6$ or $x = -8$
Find Corresponding y-Values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. We can use $y = -34x - 11$ . $\newline$ For $x = -6$ : $\newline$ $y = -34(-6) - 11$ $\newline$ $y = 204 - 11$ $\newline$ $y = 193$
Find y-Value: Find the y-value for $x = -8$ : $y = -34(-8) - 11$ $y = 272 - 11$ $y = 261$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(-6, 193)$ $\newline$ Second Coordinate: $(-8, 261)$