Answer:
Explanation:
Since, zeros of the relation are 5, 6 and y-intercept is (0, 30).
Therefore, equation of the quadratic relation will be in the form of,
y = a(x - 5)(x - 6)
For (0, 30),
30 = a(0 - 5)(0 - 6)
30 = 30a
a = 1
Therefore, equation will be,
y = (x - 5)(x - 6)
y = x² - 11x + 30
y = x²- 2(5.5)x + (5.5)² - (5.5)² + 30
y = (x - 5.5)²+ 30 - 30.25
y = (x - 5.5)² - 0.25 [Standard form}
b). Vertex → (-4, -7) and passes through a point (-2, 1)
Vertex form or standard equation of the quadratic relation is,
y = a(x - h)² + k
Here, (h, k) is the vertex
Therefore, equation will be,
y = a(x + 4)² - 7
Since, (-2, 1) lies on this relation
1 = a(-2 + 4)² - 7
a(2)²- 7 = 1
4a = 8
a = 2
Equation will be,
y = 2(x + 4)²- 7