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(b)

{:[2(1)/(2)+x=3(1)/(4)quad{:[3(1)/(4)(2)/(8)],[2(1)/(2)(4)/(8)]:}],[2(1)/(2)+1(3)/(4)(2)/(8y)]:}

(b) $\newline$ $\begin{array}{r} 2 \frac{1}{2}+x=3 \frac{1}{4} \quad \begin{array}{r} 3 \frac{1}{4} \frac{2}{8} \\ 2 \frac{1}{2} \frac{4}{8} \end{array} \\ 2 \frac{1}{2}+1 \frac{3}{4} \frac{2}{8 y} \end{array}$

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Write a quadratic function from its x-intercepts and another point

Full solution

Q. (b)

\newline

\begin{array}{r} 2 \frac{1}{2}+x=3 \frac{1}{4} \quad \begin{array}{r} 3 \frac{1}{4} \frac{2}{8} \\ 2 \frac{1}{2} \frac{4}{8} \end{array} \\ 2 \frac{1}{2}+1 \frac{3}{4} \frac{2}{8 y} \end{array}

Simplify Equations: First, let's simplify the equations. $\newline$ $2(\frac{1}{2}) + x = 3(\frac{1}{4})$ $\newline$ $3(\frac{1}{4})(\frac{2}{8}) = 3(\frac{1}{4}) \times \frac{1}{4}$ because $\frac{2}{8}$ simplifies to $\frac{1}{4}$ . $\newline$ $2(\frac{1}{2})(\frac{4}{8}) = 2(\frac{1}{2}) \times \frac{1}{2}$ because $\frac{4}{8}$ simplifies to $\frac{1}{2}$ .
Solve Simplified Equations: Now, let's solve the simplified equations. $\newline$ $1 + x = \frac{3}{4}$ $\newline$ $\frac{3}{4} \times \frac{1}{4} = \frac{3}{16}$ $\newline$ $1 \times \frac{1}{2} = \frac{1}{2}$
Solve for x: Next, we solve for x. $\newline$ $x = \frac{3}{4} - 1$ $\newline$ $x = \frac{3}{4} - \frac{4}{4}$ $\newline$ $x = -\frac{1}{4}$
Second Part of System: Now, let's look at the second part of the system. $\newline$ $2(\frac{1}{2}) + 1(\frac{3}{4})(\frac{2}{8})y = 0$ $\newline$ This simplifies to: $\newline$ $1 + \frac{3}{4} \times \frac{1}{4} \times y = 0$ $\newline$ $1 + \frac{3}{16}y = 0$
Solve for y: Finally, we solve for y. $\newline$ $\frac{3}{16}y = -1$ $\newline$ $y = -1 / \left(\frac{3}{16}\right)$ $\newline$ $y = -1 \times \frac{16}{3}$ $\newline$ $y = -\frac{16}{3}$

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