Looking at the graph, we can say that:
- It opens downward and has a maximum of 0.
- The axis of symmetry passes through the vertex (the maximum value in this case). So, the x-coordinate of the vertex is 4, and the axis of symmetry is:
- We conclude that the coordinates of the vertex are:
- The x-intercepts are defined as those points whose y-coordinate is 0. Similarly, the y-intercepts are those points of x-coordinate equal to 0. Looking at the graph, the vertex itself is the x-intercept, and y = -8 is the y-intercept.
Answer:
285.6 square units
Step-by-step explanation:
The shaded area can be described a a whole circle less a 90° segment, or as a 3/4 circle with a right triangle added. The formula for the segment area is that of a sector less the triangle, so the computation is the same either way.
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<h3>3/4 circle area</h3>
The area of a circle is given by ...
A = πr²
so 3/4 of a circle is 3/4 this value:
3/4 circle area = (3/4)(π)(10²) = 75π . . . . square units
<h3>Triangle area</h3>
The area of the isosceles right triangle is given by ...
A = 1/2s²
A = 1/2(10²) = 50 . . . . square units
<h3>Shaded area</h3>
The shaded area is the sum of these two ...
shaded area = 3/4 circle area + right triangle area
shaded area = 75π + 50 ≈ 285.6 . . . . square units
