How do you write a quadratic function in standard form whose graph passes through points (2,-7), (-2,21), (1,-3)?

Answer 1

#y = x^2 - 7 x + 3#

3 points, 3 equations, 3 variables {a, b, c}

#ax^2 + bx + c = y# #a * 2^2 + b*2 + c = -7 Rightarrow c = -7 -4a -2b# #a(-2)^2 + b(-2) + c = 21# #a*1^2 + b*1 + c = -3#
Substituting #c# in the second #4a - 2b -7 -4a - 2b = 21# #-4b = 28 Rightarrow b = -7#
Substituting #b# in #c# #c = -7 -4a + 14 = 7 - 4a#
Substituting #b# and #c# in the third #a - 7 + 7 - 4a = -3# #-3a = -3 Rightarrow a = 1#
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Answer 2

To write a quadratic function in standard form, you can use the general form ( y = ax^2 + bx + c ), where ( a ), ( b ), and ( c ) are constants.

  1. Substitute the given points into the equation to form a system of equations.
  2. Solve the system of equations to find the values of ( a ), ( b ), and ( c ).
  3. Once you have the values of ( a ), ( b ), and ( c ), substitute them into the general form equation.

For the points ( (2, -7) ), ( (-2, 21) ), and ( (1, -3) ), the system of equations would be:

[ 4a + 2b + c = -7 ] [ 4a - 2b + c = 21 ] [ a + b + c = -3 ]

Solve this system to find the values of ( a ), ( b ), and ( c ). Once you have these values, substitute them into the general form equation ( y = ax^2 + bx + c ) to get the quadratic function in standard form.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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