Question
What is the standard form equation of the graph below?
(1 point)
Responses
y=−4x2+10x+15
y is equal to negative 4 x squared plus 10 x plus 15
y=x2−6x+1
y is equal to x squared minus 6 x plus 1
y=4x2−10x+5
y is equal to 4 x squared minus 10 x plus 5
y=−2x2−16x−30
y is equal to negative 2 x squared minus 16 x minus 30
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(1 point)
Responses
y=−4x2+10x+15
y is equal to negative 4 x squared plus 10 x plus 15
y=x2−6x+1
y is equal to x squared minus 6 x plus 1
y=4x2−10x+5
y is equal to 4 x squared minus 10 x plus 5
y=−2x2−16x−30
y is equal to negative 2 x squared minus 16 x minus 30
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Answers
GPT-4o mini
To determine which of the given equations is the standard form equation of the graph, we need some key characteristics from the graph, such as the vertex, direction of opening (upwards or downwards), and any x-intercepts or y-intercepts if possible.
Unfortunately, I can't see graphs directly as a text-based model. However, I can help you analyze the equations provided based on their standard forms.
1. The vertex form of a quadratic is \(y = a(x - h)^2 + k\) where (h, k) is the vertex.
2. The standard form is \(y = ax^2 + bx + c\).
From the responses provided, we can analyze them based on the leading coefficient (a) to determine if the parabola opens upwards (if a > 0) or downwards (if a < 0):
- **Option 1:** \(y = -4x^2 + 10x + 15\) → Opens downwards (a < 0)
- **Option 2:** \(y = x^2 - 6x + 1\) → Opens upwards (a > 0)
- **Option 3:** \(y = 4x^2 - 10x + 5\) → Opens upwards (a > 0)
- **Option 4:** \(y = -2x^2 - 16x - 30\) → Opens downwards (a < 0)
Next, if you have specific points (like vertex or intercepts) or constraints from the graph itself, please provide that information, and I can help you deduce which equation is correct. Otherwise, if you can analyze the direction the graph opens and its vertex position relative to the axes, you may be able to choose the correct equation from the responses.
Unfortunately, I can't see graphs directly as a text-based model. However, I can help you analyze the equations provided based on their standard forms.
1. The vertex form of a quadratic is \(y = a(x - h)^2 + k\) where (h, k) is the vertex.
2. The standard form is \(y = ax^2 + bx + c\).
From the responses provided, we can analyze them based on the leading coefficient (a) to determine if the parabola opens upwards (if a > 0) or downwards (if a < 0):
- **Option 1:** \(y = -4x^2 + 10x + 15\) → Opens downwards (a < 0)
- **Option 2:** \(y = x^2 - 6x + 1\) → Opens upwards (a > 0)
- **Option 3:** \(y = 4x^2 - 10x + 5\) → Opens upwards (a > 0)
- **Option 4:** \(y = -2x^2 - 16x - 30\) → Opens downwards (a < 0)
Next, if you have specific points (like vertex or intercepts) or constraints from the graph itself, please provide that information, and I can help you deduce which equation is correct. Otherwise, if you can analyze the direction the graph opens and its vertex position relative to the axes, you may be able to choose the correct equation from the responses.