Question

this graph represents a quadratic function.

what is the value of a in the functions equation?

-3
-2
2
3

Explanation:

Identify the vertex from the graph

The vertex \( (h, k) \) is the lowest point of the parabola.
Looking at the grid, the vertex is located at \( (-2, 2) \).

Write the vertex form of the quadratic function

The vertex form of a quadratic function is:

$$ y = a(x - h)^2 + k $$

Substituting the vertex \( (h, k) = (-2, 2) \):

$$ y = a(x + 2)^2 + 2 $$

Identify another point on the parabola

We find a clear grid intersection point on the graph.
The parabola passes through the point \( (-1, 5) \) and also \( (-3, 5) \).

Solve for the coefficient \( a \)

Substitute the point \( (-1, 5) \) into the equation:

$$ 5 = a(-1 + 2)^2 + 2 $$

$$ 5 = a(1)^2 + 2 $$

$$ 5 = a + 2 $$

$$ a = 3 $$

Answer:

• -3
• -2
• 2
• 3 (Correct answer)