Answer :
The quadratic function's domain is all real numbers (-∞, ∞), while its range is limited to y-values greater than or equal to the vertex point. (option b)
Given that the graph opens upwards, it implies that the coefficient of the squared term in the quadratic function is positive. The general form of a quadratic function is y = ax² + bx + c, where 'a' is the coefficient of the squared term. In this context, since the parabola opens upwards, 'a' must be positive. The fact that the points (1, 6) and (2, 2) lie on the graph provides us with valuable information.
We can use these points to formulate a system of equations:
For point (1, 6):
6 = a(1)² + b(1) + c => a + b + c = 6 ...(Equation 1)
For point (2, 2):
2 = a(2)² + b(2) + c => 4a + 2b + c = 2 ...(Equation 2)
Subtracting Equation 1 from Equation 2, we get:
3a + b = -4 ...(Equation 3)
Since the coefficient 'a' is positive, we can determine that 'b' is negative from Equation 3. This is because both 'a' and 'b' have to contribute to the negative value on the right side of the equation to satisfy the condition.
Hence the correct option is (b).
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The domain is the input value which is the x values
Because the graph continues off the page in a U shape the domain is any real number.
The bottom of the U is at x = 3 and y = 2 so the range is any number greater than or equal to 2
The answer is the first choice.
