(i) The equation of the axis of symmetry is x = - 5.
(ii) The coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.
(iii) According to the <em>vertex</em> form of the <em>quadratic</em> equation, the parabola opens down due to <em>negative</em> lead coefficient and has a vertex at (2, 4), which is a <em>maximum</em>.
<h3>How to analyze and interpret quadratic functions</h3>
In this question we must find and infer characteristics from three cases of <em>quadratic</em> equations. (i) In this case we must find a formula of a axis of symmetry based on information about the vertex of the parabola. Such axis passes through the vertex. Hence, the equation of the axis of symmetry is x = - 5.
(ii) We need to transform the <em>quadratic</em> equation into its <em>vertex</em> form to determine the coordinates of the vertex by algebraic handling:
y = x² - 8 · x - 2
y + 18 = x² - 8 · x + 16
y + 18 = (x - 4)²
In a nutshell, the coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.
(iii) Now here we must apply a procedure similar to what was in used in part (ii):
y = - 2 · (x² - 4 · x + 2)
y - 4 = - 2 · (x² - 4 · x + 2) - 4
y - 4 = - 2 · (x² - 4 · x + 4)
y - 4 = - 2 · (x - 2)²
According to the <em>vertex</em> form of the <em>quadratic</em> equation, the parabola opens down due to <em>negative</em> lead coefficient and has a vertex at (2, 4), which is a <em>maximum</em>.
To learn more on quadratic equations: brainly.com/question/1863222
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