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
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