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{:[(7)/(9)-5],[y=4],[(x=4)],[-9x+5y=16]:}

$\begin{array}{c}\frac{7}{9}-5 \\ y=4 \\ (x=4) \\ -9 x+5 y=16\end{array}$

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

Full solution

Q.

\begin{array}{c}\frac{7}{9}-5 \\ y=4 \\ (x=4) \\ -9 x+5 y=16\end{array}

Simplify Fraction: First, let's simplify the fraction $(\frac{7}{9}) - 5$ . $\newline$ $(\frac{7}{9}) - 5 = (\frac{7}{9}) - (\frac{45}{9}) = \frac{-38}{9}$
Given Equation: Now, we have $y = 4$ from the given equations, so we'll keep that in mind.
Substitute $x$ : Next, we need to substitute $x = 4$ into the equation $-9x + 5y = 16$ to find $y$ .
$-9(4) + 5y = 16$
$-36 + 5y = 16$
Isolate $5y$ Term: Now, we'll add $36$ to both sides to isolate the $5y$ term. $\newline$ $-36 + 36 + 5y = 16 + 36$ $\newline$ $5y = 52$
Solve for y: Finally, we'll divide both sides by $5$ to solve for $y$ . $\frac{5y}{5} = \frac{52}{5}$ $y = 10.4$

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