What’s the missing length?
1 answer:
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Given:
The function is:
To find:
Express the quadratic equation in the form of , then state the minimum or maximum value,axis of symmetry and minimum or maximum point.
Solution:
The vertex form of a quadratic function is:
...(i)
Where, a is a constant, (h,k) is the vertex and x=h is the axis of symmetry.
We have,
It can be written as:
Adding and subtracting square of half of coefficient of x inside the parenthesis, we get
...(ii)
On comparing (i) and (ii), we get
Here, a is negative, the given function represents a downward parabola and its vertex is the point of maxima.
Maximum value = 10.125
Axis of symmetry :
Maximum point = (1.75,10.125)
Therefore, the vertex form of the given function is , the maximum value is 10.125, the axis of symmetry is
and the maximum point is (1.75,10.125).
Consider the right triangle HBF. The Pythagorean theorem tells you ...
HF² = HB² + BF²
The lengths HB and BF can be determined by counting grid squares, or by subtracting coordinates. Here, it is fairly convenient to count grid squares. When we do that, we find ...
HB = 2
BF = 5
Using these values in the equation above, we get
HF² = 2² + 5²
HF² = 4 + 25 = 29
Taking the square root gives the length HF.
HF = √29
HF² = HB² + BF²
The lengths HB and BF can be determined by counting grid squares, or by subtracting coordinates. Here, it is fairly convenient to count grid squares. When we do that, we find ...
HB = 2
BF = 5
Using these values in the equation above, we get
HF² = 2² + 5²
HF² = 4 + 25 = 29
Taking the square root gives the length HF.
HF = √29