Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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![## Graph Analysis and X-Intercept Calculation
### Function Graphs and Instructions
**Function 5:**
\[ y = x^2 + 2x + 2 \]
**Function 6:**
\[ y = x^2 + 2x + 4 \]
### Graph Descriptions:
#### Graph for Function 5:
- Title: \( y = x^2 + 2x + 2 \)
- This is a parabolic curve opening upwards.
- The vertex of the parabola is the minimum point on the graph.
- The graph intersects the y-axis at \( y = 2 \).
- Identifying x-intercepts (where the curve crosses the x-axis) is requested.
#### Graph for Function 6:
- Title: \( y = x^2 + 2x + 4 \)
- This is also a parabolic curve opening upwards.
- Similarly, it has its vertex at the minimum point.
- The graph intersects the y-axis at \( y = 4 \).
- Identifying x-intercepts is requested for this function as well.
### Instruction Text:
**Find EXACT VALUES of x-intercepts for EACH function graphed below!**
### Steps to Find the X-Intercepts:
1. **For Function 5:**
- Set \( y = 0 \) in the equation \( y = x^2 + 2x + 2 \).
- Solve the quadratic equation \( x^2 + 2x + 2 = 0 \).
2. **For Function 6:**
- Set \( y = 0 \) in the equation \( y = x^2 + 2x + 4 \).
- Solve the quadratic equation \( x^2 + 2x + 4 = 0 \).
### Solving Quadratic Equations:
Use the quadratic formula to find the x-intercepts:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Where \( a = 1, b = 2, \) and \( c = 2 \) for Function 5 and \( c = 4 \) for Function 6.
#### Example Calculation for Function 5:
\[ x = \frac{-2 \pm \sqrt{2^2 - 4 \cdot 1 \cdot 2}}{2 \cdot 1}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ce901d6-1005-4fae-945e-8fe9887caefc%2Fd3609694-fa92-4f3e-a29c-fe0f6f2d9bae%2Fqobrmnl_processed.png&w=3840&q=75)
Step by step
Solved in 2 steps with 2 images
