a system of equations is graphed here. which system of equations does the graph represent? A) y = 3x + 2y = -2x + 5 B) y = 3x -
2 y = 2x + 5 C) y = -3x + 2 y = 2x - 5 D) y = -3x - 2 y = -2x - 5
1 answer:
Notice that the line with negative slope has a y-intercept of 5 and the line with positive slope has a y-intercept of 2.
On the other hand, the slope of the line with negative slope is -2, while the slope of the line with positive slope is 3 (This can be identified since in one case, the value of y decreases by 2 for each increase of 1 unit in x, and in the other, the value of y increases by 3 for each increase of 1 unit in x).
Using the y-intercept form to represent each line, the system of equations represented by the graph must be equivalent to:
From the given options, the one that displays the correct system of equations is option A.
Therefore, the answer is:
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Answer:
(- 1, 2)
Step-by-step explanation:
Given a quadratic in standard form y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
= -
f(x) = x² + 2x + 3 ← is in standard form
with a = 1 and b = 2, hence
= -
= - 1
Substitute x = - 1 into f(x) for corresponding value of y
f(- 1) = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2
vertex = (- 1, 2 )