The extreme value of y = (x - h)² - c is the vertex of the equation.
<h3>What are extreme values of a function?</h3>
The extreme values of a function are either the maximum or minimum values of the function.
<h3>The equation of a parabola in vertex form</h3>
The equation of a parabola in vertex form with vertex (h', k) is given by
y = a(x - h')² + k and its extreme values are
- if a > 0 (h', k) is a minimum point and
- if a < 0 (h', k) is a maximum point.
Since y = (x - h)² - c is the equation of a parabola in vertex form, comparing with y = a(x - h')² + k,
So, the cooordinates of the vertex of y = (x - h)² - c is (h, -c).
Now, since a = 1 > 0, (h, -c) is a minimum point.
So, the extreme value of y = (x - h)² - c is the vertex of the equation.
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The unit rate in this problem is one payment per month. Since Martha has made 86 payments, that means it has been 86 months. Because of that, we can simply multiply 3335*86 to get 286810.
So she so far has paid $286,810 for her house payment
- A function that models the data is given by this quadratic equation, y = -0.4908x² + 5.8845x + 1.3572.
- The number of students that are absent 10 days after the outbreak is equal to 11 students.
<h3>What is a scatter plot?</h3>
A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association (correlation) between the data set.
<h3>What is a quadratic function?</h3>
A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the quadratic function is given by:
y = -0.4908x² + 5.8845x + 1.3572
For the number of students that are absent 10 days after the outbreak, we have:
y = -0.4908(10)² + 5.8845(10) + 1.3572
y = -0.4908(100) + 58.845 + 1.3572
y = -49.08 + 58.845 + 1.3572
Number of students, y = 11.12 ≈ 11 students.
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Step-by-step explanation:
area of trapezoid = 1/2 × (a+b) h
where a = long base
b = short base
h = height
given that, a = 8, b = 5, a of trapezoid = 104:
area of trapezoid = 1/2 × ( 8+5) h
104 = 13/2 h
104 * 2 = 13 h
13 h = 208
h = 208 / 13
h = 16.0 ft.
hope this helps you!
-s.