Solve the system of equations. y = x^2 - 10x + 30 y = -25x - 20 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. y = x^2 - 10x + 30 y = -25x - 20 x^2 - 10x + 30 = -25x - 20Form Quadratic Equation: Move all terms to one side to form a quadratic equation. x^2 - 10x + 25x + 30 + 20 = 0 x^2 + 15x + 50 = 0Factor Quadratic: Factor the quadratic equation. (x + 5)(x + 10) = 0Solve for x: Set each factor equal to zero and solve for x. x + 5 = 0 or x + 10 = 0 x = -5 or x = -10Substitute x = -5: Substitute x = -5 into one of the original equations to find y. y = -25(-5) - 20 y = 125 - 20 y = 105Substitute x = -10: Substitute x = -10 into one of the original equations to find y. y = -25(-10) - 20 y = 250 - 20 y = 230

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Solve the system of equations. $\newline$ $y = x^2 - 10x + 30$ $\newline$ $y = -25x - 20$ $\newline$ 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 - 10x + 30

\newline

y = -25x - 20

\newline

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 $y$ . $y = x^2 - 10x + 30$ $y = -25x - 20$ $x^2 - 10x + 30 = -25x - 20$
Form Quadratic Equation: Move all terms to one side to form a quadratic equation. $\newline$ $x^2 - 10x + 25x + 30 + 20 = 0$ $\newline$ $x^2 + 15x + 50 = 0$
Factor Quadratic: Factor the quadratic equation. $\newline$ $(x + 5)(x + 10) = 0$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $x + 5 = 0$ or $x + 10 = 0$ $\newline$ $x = -5$ or $x = -10$
Substitute $x = -5$ : Substitute $x = -5$ into one of the original equations to find $y$ . $\newline$ $y = -25(-5) - 20$ $\newline$ $y = 125 - 20$ $\newline$ $y = 105$
Substitute $x = -10$ : Substitute $x = -10$ into one of the original equations to find $y$ . $\newline$ $y = -25(-10) - 20$ $\newline$ $y = 250 - 20$ $\newline$ $y = 230$