Solve the system of equations. y = 7x^2 + 8x + 25 y = 8x + 32 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: Set the two equations equal to each other to find the x-values where the graphs intersect. 7x^2 + 8x + 25 = 8x + 32Subtract and Simplify: Subtract 8x + 32 from both sides to move all terms to one side and set the equation to zero. 7x^2 + 8x + 25 - 8x - 32 = 0 7x^2 + 25 - 32 = 0 7x^2 - 7 = 0Factor and Solve: Factor out the common term and solve for x. 7(x^2 - 1) = 0 x^2 - 1 = 0 This is a difference of squares, which can be factored further. (x + 1)(x - 1) = 0Set Factors Equal: Set each factor equal to zero and solve for x. x + 1 = 0 or x - 1 = 0 x = -1 or x = 1Substitute and Find: Substitute the x-values back into either original equation to find the corresponding y-values. For x = -1: y = 8(-1) + 32 y = -8 + 32 y = 24 For x = 1: y = 8(1) + 32 y = 8 + 32 y = 40Write Coordinates: Write the coordinates in exact form. First Coordinate: (-1, 24) Second Coordinate: (1, 40)

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Solve the system of equations. $\newline$ $y = 7x^2 + 8x + 25$ $\newline$ $y = 8x + 32$ $\newline$ 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

Full solution

Q. Solve the system of equations.

\newline

y = 7x^2 + 8x + 25

\newline

y = 8x + 32

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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 to find the $x$ -values where the graphs intersect. $7x^2 + 8x + 25 = 8x + 32$
Subtract and Simplify: Subtract $8x + 32$ from both sides to move all terms to one side and set the equation to zero. $\newline$ $7x^2 + 8x + 25 - 8x - 32 = 0$ $\newline$ $7x^2 + 25 - 32 = 0$ $\newline$ $7x^2 - 7 = 0$
Factor and Solve: Factor out the common term and solve for $x$ . $7(x^2 - 1) = 0$ $x^2 - 1 = 0$ This is a difference of squares, which can be factored further. $(x + 1)(x - 1) = 0$
Set Factors Equal: Set each factor equal to zero and solve for $x$ . $x + 1 = 0$ or $x - 1 = 0$ $x = -1$ or $x = 1$
Substitute and Find: Substitute the $x$ -values back into either original equation to find the corresponding $y$ -values. $\newline$ For $x = -1$ : $\newline$ $y = 8(-1) + 32$ $\newline$ $y = -8 + 32$ $\newline$ $y = 24$ $\newline$ For $x = 1$ : $\newline$ $y = 8(1) + 32$ $\newline$ $y = 8 + 32$ $\newline$ $y = 40$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(-1, 24)$ $\newline$ Second Coordinate: $(1, 40)$