Question

You are asked to graph a
parabola on a coordinate
plane given the equation y=-1/8x^2 + 3/4x + 7/8
. Fill in
the missing value on the table
for the coordinates of the
parabola. (1 point)

x-value y-value
0
3 2
0
11
You are asked to graph a
parabola on a coordinate
plane given the equation
. Fill in
the missing value on the table
for the coordinates of the
parabola. (1 point)
1
8x
2 3
4
7
8
−1
−6

Answer 1

To fill in the missing values for the given equation of the parabola \( y = -\frac{1}{8}x^2 + \frac{3}{4}x + \frac{7}{8} \), let's calculate the \( y \)-values for the specified \( x \)-values.

### Given Values:
1. **When \( x = 0 \)**:
\[
y = -\frac{1}{8}(0)^2 + \frac{3}{4}(0) + \frac{7}{8} = \frac{7}{8}
\]

2. **When \( x = 3 \)**:
\[
y = -\frac{1}{8}(3)^2 + \frac{3}{4}(3) + \frac{7}{8}
\]
\[
= -\frac{1}{8} \cdot 9 + \frac{9}{4} + \frac{7}{8}
\]
Converting \(\frac{9}{4}\) to an eighths denominator:
\[
\frac{9}{4} = \frac{18}{8}
\]
So:
\[
y = -\frac{9}{8} + \frac{18}{8} + \frac{7}{8} = \frac{16}{8} = 2
\]

3. The \( y \)-values:
- For \( x = 0 \): \( y = \frac{7}{8} \)
- For \( x = 3 \): \( y = 2 \)

### Now for the next part:
For smaller values of \( x \) and the larger one:

1. **When \( x = 1 \)**:
\[
y = -\frac{1}{8}(1)^2 + \frac{3}{4}(1) + \frac{7}{8}
\]
\[
= -\frac{1}{8} + \frac{3}{4} + \frac{7}{8}
\]
Converting \(\frac{3}{4}\) to an eighths denominator:
\[
\frac{3}{4} = \frac{6}{8}
\]
So:
\[
y = -\frac{1}{8} + \frac{6}{8} + \frac{7}{8} = \frac{12}{8} = \frac{3}{2}
\]

2. **When \( x = 4 \)**:
\[
y = -\frac{1}{8}(4)^2 + \frac{3}{4}(4) + \frac{7}{8}
\]
\[
= -\frac{1}{8} \cdot 16 + 3 + \frac{7}{8}
\]
So:
\[
y = -2 + 3 + \frac{7}{8} = 1 + \frac{7}{8} = \frac{15}{8}
\]

3. **When \( x = 7 \)**:
\[
y = -\frac{1}{8}(7)^2 + \frac{3}{4}(7) + \frac{7}{8}
\]
\[
= -\frac{1}{8} \cdot 49 + \frac{21}{4} + \frac{7}{8}
\]
Converting \(\frac{21}{4}\) to an eighths denominator:
\[
\frac{21}{4} = \frac{42}{8}
\]
So:
\[
y = -\frac{49}{8} + \frac{42}{8} + \frac{7}{8} = -\frac{49 - 42 - 7}{8} = -\frac{49 - 49}{8} = 0
\]

4. **When \( x = 11 \)**:
\[
y = -\frac{1}{8}(11)^2 + \frac{3}{4}(11) + \frac{7}{8}
\]
\[
= -\frac{121}{8} + \frac{33}{4} + \frac{7}{8}
\]
Converting \(\frac{33}{4}\) to an eighths denominator:
\[
\frac{33}{4} = \frac{66}{8}
\]
So:
\[
y = -\frac{121}{8} + \frac{66}{8} + \frac{7}{8} = -\frac{121 - 66 - 7}{8} = -\frac{121 - 73}{8} = -\frac{48}{8} = -6
\]

### Summary of Calculated Points:
- \( (0, \frac{7}{8}) \)
- \( (3, 2) \)
- \( (1, \frac{3}{2}) \)
- \( (4, \frac{15}{8}) \)
- \( (7, 0) \)
- \( (11, -6) \)

### Table Completion:
```
| x-value | y-value |
|---------|--------------|
| 0 | 7/8 |
| 3 | 2 |
| 1 | 3/2 |
| 4 | 15/8 |
| 7 | 0 |
| 11 | -6 |
```

Now you have the filled in values for the parabola!