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Write the equation in standard form f(x)=ax2+bx+cf (x) = ax^2 + bx + c. By using given points: (−10,10)(-10, 10), (−7,4)(-7, 4), (−11,20)(-11, 20)

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Write a quadratic function from its x-intercepts and another pointright chevron icon

Full solution

Q. Write the equation in standard form f(x)=ax2+bx+cf (x) = ax^2 + bx + c. By using given points: (−10,10)(-10, 10), (−7,4)(-7, 4), (−11,20)(-11, 20)
  1. Plug and Simplify Quadratic Equation: Let's use the general form of a quadratic equation f(x)=ax2+bx+cf(x) = ax^2 + bx + c and plug in the points to get three equations.
  2. Eliminate Constant Term: Simplify each equation.
  3. Align and Eliminate bb Term: Subtract the second equation from the first to eliminate cc.
  4. Correct Mistake in Elimination: Subtract the second equation from the third to eliminate cc.
  5. Correct Mistake in Elimination: Subtract the second equation from the third to eliminate cc. Multiply the third step's equation by 33 and the fourth step's equation by 44 to align the bb terms.
  6. Correct Mistake in Elimination: Subtract the second equation from the third to eliminate cc. Multiply the third step's equation by 33 and the fourth step's equation by 44 to align the bb terms. Subtract the fifth step's equation from the sixth step's equation to eliminate bb.
  7. Correct Mistake in Elimination: Subtract the second equation from the third to eliminate cc. Multiply the third step's equation by 33 and the fourth step's equation by 44 to align the bb terms. Subtract the fifth step's equation from the sixth step's equation to eliminate bb. There's a mistake in the previous step, we didn't actually eliminate bb. Let's correct that.

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