Answer:
The quadratic function, \(y=x^{2}\), has an x-intercept at the origin
From \(x = -2\) to \(x = 0\), the average rate of change for both functions is negative
For the quadratic function, \(y=x^{2}+3\), the coordinate \((2, 7)\) is a solution to the equation of the function
Step-by-step explanation:
we have the quadratic functions
\(y=x^{2}\)
\(y=x^{2}+3\)
Verify each statement
case A) The quadratic function, \(y=x^{2}\), has an x-intercept at the origin
Remember that
The x-intercept is the value of x when the value of y is equal to zero
The point \((0,0)\) represent and x-intercept and a y-intercept
therefore
The statement is True
case B) The quadratic function, \(y=x^{2}+3\), has an x-intercept at the origin
The quadratic function, \(y=x^{2}+3\) has no x-intercept
so
The statement is False
case C) From \(x = -2\) to \(x = 0\), the average rate of change for both functions is positive
Observing the graph from \(x = -2\) to \(x = 0\), the average rate of change for both functions is negative
so
The statement is False
case D) From \(x = -2\) to \(x = 0\), the average rate of change for both functions is negative
The statement is True
case E) For the quadratic function, \(y=x^{2}\), the coordinate \((2, 3)\) is a solution to the equation of the function
we know that
If a ordered pair is a solution of the quadratic function
then
the ordered pair must be satisfy the quadratic equation
Substitute the value of x and the value of y in the quadratic function and then compare
\(3=2^{2}\)
\(3=4\) ------> is not true
The ordered pair is not a solution
so
The statement is False
case F) For the quadratic function, \(y=x^{2}+3\), the coordinate \((2, 7)\) is a solution to the equation of the function
we know that
If a ordered pair is a solution of the quadratic function
then
the ordered pair must be satisfy the quadratic equation
Substitute the value of x and the value of y in the quadratic function and then compare
\(7=2^{2}+3\)
\(7=7\) ------> is true
The ordered pair is a solution
so
The statement is True
