Considering the equation of the circle graphed on this problem, the value of y is given by:
[tex]y = -\frac{1}{4}[/tex]
What is the equation of a circle?
The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In this problem, the circle is centered at the origin, with radius 1, hence the equation is given by:
[tex]x^2 + y^2 = 1[/tex]
Hence, when [tex]x = -\frac{\sqrt{15}}{4}[/tex], the values of y are given by:
[tex]y^2 = 1 - x^2[/tex]
[tex]y^2 = 1 - \frac{15}{16}[/tex]
[tex]y^2 = \frac{1}{16}[/tex]
Looking at the graph, we want the negative value of y, hence:
[tex]y = -\sqrt{\frac{1}{16}}[/tex]
[tex]y = -\frac{1}{4}[/tex]
More can be learned about the equation of a circle at https://brainly.com/question/24307696
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