Use the image to answer the question.

Question

A coordinate plane shows a parabola that opens downward. The x-axis ranges from 0 to 15 in increments of 5. The y-axis ranges from 0 to 15 in increments of 5.

The graph shows the trajectory of a firework. Which equation in vertex form matches this graph?

(1 point)
Responses

y=12(x+5)2+10
y equals Start Fraction 1 over 2 End Fraction left parenthesis x plus 5 right parenthesis squared plus 10

y=−12(x−5)2+10
y equals negative Start Fraction 1 over 2 End Fraction left parenthesis x minus 5 right parenthesis squared plus 10

y=12(x−5)2+10
y equals Start Fraction 1 over 2 End Fraction left parenthesis x minus 5 right parenthesis squared plus 10

y=−12(x−5)2−10

Answer 1

To determine which equation in vertex form matches the graph, we need to analyze the characteristics of the parabola portrayed in the graph.

1. Direction of the parabola: Since the parabola opens downward, the coefficient in front of the squared term must be negative.

2. Vertex of the parabola: The vertex form is given by \( y = a(x - h)^2 + k \), where (h, k) is the vertex of the parabola. According to the responses you provided, we can identify the vertex points from the equation.

   • If the vertex is at (5, 10), the vertex form would look something like \( y = a(x - 5)^2 + 10 \).
   • If the vertex is at (-5, 10), the vertex form would then be \( y = a(x + 5)^2 + 10 \).

Since the correct vertex will guide us towards the right equation, we will check the provided options:

• y=12(x+5)²+10: This opens upwards.
• y=−12(x−5)²+10: This opens downwards with a vertex at (5, 10).
• y=12(x−5)²+10: This opens upwards.
• y=−12(x−5)²−10: This opens downwards but has a vertex at (5, -10).

Given that the parabola opens downwards, the only equation that fits all these criteria with a vertex at (5, 10) is:

y=−12(x−5)²+10

Therefore, the correct answer is:

y = −12(x - 5)² + 10.