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Write a quadratic equation in standard form given zeros {-7,3}

User Nlogax
by
7.2k points

2 Answers

6 votes

Answer:


y=x^2+4x-21

Explanation:


\boxed{\begin{minipage}{6 cm}\underline{Factored form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the zeros. \\ \phantom{ww}$\bullet$ $a$ is the leading coefficient.\\\end{minipage}}

Given zeros:

  • -7 and 3

Substitute the given zeros into the formula:


\implies y=a(x-(-7))(x-3)


\implies y=a(x+7)(x-3)

The value of "a" will not change the zeros, therefore let "a" equal any value:


\implies y=1(x+7)(x-3)


\implies y=(x+7)(x-3)

Standard form of a quadratic equation:


\boxed{y=ax^2+bx+c}

Therefore, to write the equation in standard form, expand the brackets and simplify:


\implies y=x(x-3)+7(x-3)


\implies y=x^2-3x+7x-21


\implies y=x^2+4x-21

User Ltamajs
by
7.9k points
4 votes

Answer:

  • y = x² + 4x - 21

=============================

Quadratic equation with zeros x₁ and x₂ is:

  • y = (x - x₁)(x - x₂)

And the standard form is:

  • y = ax² + bx + c

Substitute zeros and convert the equation to standard form:

  • y = (x - (-7))(x - 3)
  • y = (x + 7)(x - 3)
  • y = x² - 3x + 7x - 21
  • y = x² + 4x - 21
User Marko Vranjkovic
by
8.8k points

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