Question

Please help ty:)

Answer 1

The quadratic function in standard form that passes through ( - 2, 0 ), ( 4, 18 ), and ( 10, 0 ) is y = ( - 1/2 ) x² + 4x + 10.

The standard form of a quadratic equation is given as:

ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.

Now, the equation passes through ( - 2, 0 ).

y = ax² + bx + c

0 = 4a - 2b + c                                                                          ----------------(1)

The equation passes through ( 4, 18 ).

y = ax² + bx + c

18 = 16a + 4b + c                                                                      ----------------(2)

The equation passes through ( 10, 0 ).

y = ax² + bx + c

0 = 100a + 10b + c                                                                       ----------------(3)

Using the Gauss elimination method to solve the system of equations we get,

a = -1/2, b = 4, and c = 10

Hence, the quadratic equation will be:

y = ax² + bx + c

y = ( - 1/2 ) x² + 4x + 10

Learn more about quadratic function here:

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