Given the figure below, find the values of x and z
1 answer:
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Answer:
Option (2)
Step-by-step explanation:
Given expression is, y = (x + 3)² + (x + 4)²
By solving this expression,
y = x² + 6x + 9 + x² + 8x + 16
y = 2x² + 14x + 25
y = (2x² + 14x) + 25
y = 2(x² + 7x) + 25
y = 2[x² + 2(3.5x) + (3.5)² - (3.5)²] + 25
y = 2[x² + 2(3.5x) + (3.5)²] - 2(3.5)² + 25
y = 2(x + 3.5)² - 24.5 + 25
y = 2(x + 3.5)² + 0.5
Therefore, Option (2) will be the vertex form.
Answer:
Degree of the function = 5
y-intercept = (0, 12)
Step-by-step explanation:
Degree of a polynomial function is determined by the degree of the term having highest degree.
In the given function,
f(x) = -(x + 1)²(2x - 3)(x + 2)²
(x + 1)² → highest degree term = x²
(2x - 3) → highest degree term = x
(x + 2)² → highest degree term = x²
When we multiply these terms,
(x + 1)²(2x - 3)(x + 2)² highest degree term of the function will be,
Therefore, degree of the function = 5
For y-intercept,
f(0) = -(0 + 1)²(0 - 3)(0 + 2)² = 12
Therefore, y-intercept of the function is (0, 12)