The quadratic function f(x) has a vertex at (9, 8) and opens upward. If g(x) = 4(x − 8)2 + 9, which statement is true?
1 answer:
ANSWER
D.
The minimum value of g(x) is greater than the minimum value of f(x).
EXPLANATION
It was given that;
has a vertex at
and opens upwards.
This means that f(x) is a minimum graph and hence have a minimum value of 8.
Also ,
When we compare this function to
We can see that,a=4, h=8 and y=9.
The vertex is
Since a>0, the graph opens upwards.
The graph has a minimum point which is (8,9) and hence the minimum value is 9.
We can see that, the minimum value of g(x) is greater than the minimum value of f(x).
Therefore the correct answer is D.
D.
The minimum value of g(x) is greater than the minimum value of f(x).
EXPLANATION
It was given that;
has a vertex at
and opens upwards.
This means that f(x) is a minimum graph and hence have a minimum value of 8.
Also ,
When we compare this function to
We can see that,a=4, h=8 and y=9.
The vertex is
Since a>0, the graph opens upwards.
The graph has a minimum point which is (8,9) and hence the minimum value is 9.
We can see that, the minimum value of g(x) is greater than the minimum value of f(x).
Therefore the correct answer is D.
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Answer:
The standard equation of the parabola is:
Step-by-step explanation:
An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.
We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.
Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:
Then the equation of the parabola becomes: