Answer:
y = x²-12x + 44
Step-by-step explanation:
Given the vertex occurring at point (6, 8), and one of the points on the graph, (4, 4):
Substitute these values into the vertex form:
y = a(x - h)² + k
where:
(h, k) = vertex = (6, 8)
a = determines whether the graph opens up (positive value) or down (negative value). It also makes the parent function wider or narrower.
y = a(x - h)² + k
4 = a(4 - 6)² + 8
4 = a(-2)² + 8
4 = 4a + 8
4 - 8 = 4a + 8 - 8
-4 = 4a
Divide both sides by 4:
-4/4 = 4a/4
-1 = a
Therefore, the value of a = -1, which confirms that the graph opens downward.
Thus, the vertex form of the graph is: y = - (x + 6)² + 8
Next, transform the vertex form into standard form, y = ax² + bx + c, by expanding the binomial expression:
y = -(x + 6) -(x + 6) + 8
y = x² - 6x - 6x + 36 + 8
y = x² - 12x + 44 ← This is the standard form of the graph. Therefore, the correct answer is Option 1.
