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# Which equation represents a graph with a vertex at (-3, 2)?

y = 4x^{2} + 24x + 38

y = 4x^{2} - 24x + 38

y = 4x^{2} + 12x + 2

y = 4x^{2} + 16x + 13

**Solution:**

Given vertex at (-3,2)

Consider y = 4x^{2} + 24x + 38

y = 4x^{2} + 24x + 38

y = 4x^{2} + 24x + 36 + 2

y = (2x + 6)² + 2

y = 2²(x + 3)² + 2

y = 4(x - (-3))² + 2

This is the vertex equation y= a(x - h)² + k where (h, k) is the vertex.

## Which equation represents a graph with a vertex at (-3, 2)? y = 4x^{2} + 24x + 38

**Summary:**

The equation y= 4x^{2} + 24x + 38 represents the graph with vertex (-3, 2).

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