Question
What is the standard form equation of the graph below?
graph shows a line passing through -5 and -3 and a curve at -5,2
(1 point)
Responses
y=−2x2−16x−30
y is equal to negative 2 x squared minus 16 x minus 30
y=4x2−10x+5
y is equal to 4 x squared minus 10 x plus 5
y=x2−6x+1
y is equal to x squared minus 6 x plus 1
y=−4x2+10x+15
graph shows a line passing through -5 and -3 and a curve at -5,2
(1 point)
Responses
y=−2x2−16x−30
y is equal to negative 2 x squared minus 16 x minus 30
y=4x2−10x+5
y is equal to 4 x squared minus 10 x plus 5
y=x2−6x+1
y is equal to x squared minus 6 x plus 1
y=−4x2+10x+15
Answers
GPT-4o mini
To find the correct standard form equation for the graph described, we need to identify the features it presents: a linear component and a quadratic component.
From your description, it appears there is a line passing through the points (-5, -3) and a curve touching the point (-5, 2).
For a quadratic equation of the form \( y = ax^2 + bx + c \):
1. **Using the points**:
- The curve passes through (-5, 2), meaning when \( x = -5 \), then \( y = 2 \).
- You can substitute \( x = -5 \) into the potential equations to see if they yield \( y = 2 \).
Let’s check each equation at \( x = -5 \):
1. **For \( y = -2x^2 - 16x - 30 \)**:
\[
y = -2(-5)^2 - 16(-5) - 30 = -2(25) + 80 - 30 = -50 + 80 - 30 = 0 \quad (\text{not } 2)
\]
2. **For \( y = 4x^2 - 10x + 5 \)**:
\[
y = 4(-5)^2 - 10(-5) + 5 = 4(25) + 50 + 5 = 100 + 50 + 5 = 155 \quad (\text{not } 2)
\]
3. **For \( y = x^2 - 6x + 1 \)**:
\[
y = (-5)^2 - 6(-5) + 1 = 25 + 30 + 1 = 56 \quad (\text{not } 2)
\]
4. **For \( y = -4x^2 + 10x + 15 \)**:
\[
y = -4(-5)^2 + 10(-5) + 15 = -4(25) - 50 + 15 = -100 - 50 + 15 = -135 \quad (\text{not } 2)
\]
None of the equations include the required point (-5, 2).
Since we’re considering a curve, it’s worth noting that for a quadratic function, it typically involves a parabola, which can intercept or simply pass by points like (-5, 2). However, it seems that the equations given don't match this point.
We also need to clarify if the curve is to be quadratic because you mention a line passing through (-5, -3) which may offset the values a bit.
**Conclusion**: The listed equations do not satisfy the conditions of the graph as given.
If you can provide more details or clarify the points the line passes through (other than (-5, -3)), we can ensure to derive an appropriate equation.
From your description, it appears there is a line passing through the points (-5, -3) and a curve touching the point (-5, 2).
For a quadratic equation of the form \( y = ax^2 + bx + c \):
1. **Using the points**:
- The curve passes through (-5, 2), meaning when \( x = -5 \), then \( y = 2 \).
- You can substitute \( x = -5 \) into the potential equations to see if they yield \( y = 2 \).
Let’s check each equation at \( x = -5 \):
1. **For \( y = -2x^2 - 16x - 30 \)**:
\[
y = -2(-5)^2 - 16(-5) - 30 = -2(25) + 80 - 30 = -50 + 80 - 30 = 0 \quad (\text{not } 2)
\]
2. **For \( y = 4x^2 - 10x + 5 \)**:
\[
y = 4(-5)^2 - 10(-5) + 5 = 4(25) + 50 + 5 = 100 + 50 + 5 = 155 \quad (\text{not } 2)
\]
3. **For \( y = x^2 - 6x + 1 \)**:
\[
y = (-5)^2 - 6(-5) + 1 = 25 + 30 + 1 = 56 \quad (\text{not } 2)
\]
4. **For \( y = -4x^2 + 10x + 15 \)**:
\[
y = -4(-5)^2 + 10(-5) + 15 = -4(25) - 50 + 15 = -100 - 50 + 15 = -135 \quad (\text{not } 2)
\]
None of the equations include the required point (-5, 2).
Since we’re considering a curve, it’s worth noting that for a quadratic function, it typically involves a parabola, which can intercept or simply pass by points like (-5, 2). However, it seems that the equations given don't match this point.
We also need to clarify if the curve is to be quadratic because you mention a line passing through (-5, -3) which may offset the values a bit.
**Conclusion**: The listed equations do not satisfy the conditions of the graph as given.
If you can provide more details or clarify the points the line passes through (other than (-5, -3)), we can ensure to derive an appropriate equation.