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$Algebra 1 Y. Write a quadratic function from its x-intercepts and another point UDo You have prizes to reveall ge te youc.game : Write the equation of the parabola that passes through the points shown in the table. x y -2 15 -1 0 1 0 Write your answer in the form y=a(x-p)(x-q), where a,p, and q are integers, decimals, or simplified fractions. Submit Work it out Not feeling ready yet? These can help: Solve one-step linear equations Lesson: Quadratic equations Practice in the app$

Algebra $1$ $\newline$ Y. Write a quadratic function from its $x$ -intercepts and another point $\newline$ UDo $\newline$ You have prizes to reveall ge te youc.game : $\newline$ Write the equation of the parabola that passes through the points shown in the table. $\newline$ \begin{tabular}{|c|c|} $\newline$ \hline $x$ & $y$ \\ $\newline$ \hline $-2$ & $15$ \\ $\newline$ \hline $-1$ & $0$ \\ $\newline$ \hline $1$ & $0$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ Write your answer in the form $\mathrm{y}=\mathrm{a}(\mathrm{x}-\mathrm{p})(\mathrm{x}-\mathrm{q})$ , where $\mathrm{a}, \mathrm{p}$ , and $\mathrm{q}$ are integers, decimals, or simplified fractions. $\newline$ Submit $\newline$ Work it out $\newline$ Not feeling ready yet? These can help: $\newline$ Solve one-step linear equations $\newline$ Lesson: Quadratic equations $\newline$ Practice in the app

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Math Problems

Algebra 2

Descartes' Rule of Signs

Full solution

Q. Algebra

1

\newline

Y. Write a quadratic function from its

x

-intercepts and another point

\newline

UDo

\newline

You have prizes to reveall ge te youc.game :

\newline

Write the equation of the parabola that passes through the points shown in the table.

\newline

\begin{tabular}{|c|c|}

\newline

\hline

x

y

\newline

\hline

-2

15

\newline

\hline

-1

0

\newline

\hline

1

0

\newline

\hline

\newline

\end{tabular}

\newline

Write your answer in the form

\mathrm{y}=\mathrm{a}(\mathrm{x}-\mathrm{p})(\mathrm{x}-\mathrm{q})

, where

\mathrm{a}, \mathrm{p}

, and

\mathrm{q}

are integers, decimals, or simplified fractions.

\newline

Submit

\newline

Work it out

\newline

Not feeling ready yet? These can help:

\newline

Solve one-step linear equations

\newline

Lesson: Quadratic equations

\newline

Practice in the app

Identify x-intercepts: Identify the x-intercepts from the table. $\newline$ The x-intercepts are the points where the graph of the parabola crosses the x-axis, which means the y-value is $0$ . From the table, we can see that the x-intercepts are at $x = -1$ and $x = 1$ .
Write in factored form: Write the quadratic function in factored form using the x-intercepts. $\newline$ The general form of a quadratic function in factored form is $y = a(x - p)(x - q)$ , where $p$ and $q$ are the x-intercepts. Since we have the x-intercepts as $-1$ and $1$ , we can write the function as $y = a(x + 1)(x - 1)$ .
Find 'a' value: Use the third point to find the value of 'a'. $\newline$ We have another point $(-2, 15)$ that lies on the parabola. We can substitute $x = -2$ and $y = 15$ into the equation to solve for 'a'. $\newline$ $15 = a(-2 + 1)(-2 - 1)$ $\newline$ $15 = a(-1)(-3)$ $\newline$ $15 = 3a$ $\newline$ $a = \frac{15}{3}$ $\newline$ $a = 5$
Write final equation: Write the final equation of the parabola. $\newline$ Now that we have found the value of 'a', we can write the final equation of the parabola: $\newline$ $y = 5(x + 1)(x - 1)$