Ву З.

Create a table of volves with atleast A ports. Determare the x-andy intercepts. Then steth

Thi graph.

1) (f) = -5x-9

2） f(x)= 2×+7×-4

To solve these two functions, we need to:

1. **Find the x- and y-intercepts** for each function.
2. **Sketch the graphs**.

### Function 1: \( f(x) = -5x - 9 \)

This is a linear function of the form \( y = mx + b \), where:
- \( m = -5 \) (slope),
- \( b = -9 \) (y-intercept).

#### 1.1. X-intercept
The x-intercept occurs when \( y = 0 \). Set \( f(x) = 0 \):

\[
0 = -5x - 9
\]
\[
5x = -9
\]
\[
x = -\frac{9}{5}
\]

So, the x-intercept is \( \left( -\frac{9}{5}, 0 \right) \).

#### 1.2. Y-intercept
The y-intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into \( f(x) \):

\[
f(0) = -5(0) - 9 = -9
\]

So, the y-intercept is \( (0, -9) \).

### Function 2: \( f(x) = 2x^2 + 7x - 4 \)

This is a quadratic function of the form \( f(x) = ax^2 + bx + c \), where:
- \( a = 2 \),
- \( b = 7 \),
- \( c = -4 \).

#### 2.1. X-intercepts
To find the x-intercepts, set \( f(x) = 0 \):

\[
2x^2 + 7x - 4 = 0
\]

We can solve this quadratic equation using the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Substitute \( a = 2 \), \( b = 7 \), and \( c = -4 \):

\[
x = \frac{-7 \pm \sqrt{7^2 - 4(2)(-4)}}{2(2)}
\]
\[
x = \frac{-7 \pm \sqrt{49 + 32}}{4}
\]
\[
x = \frac{-7 \pm \sqrt{81}}{4}
\]
\[
x = \frac{-7 \pm 9}{4}
\]

So, the two solutions are:
\[
x = \frac{-7 + 9}{4} = \frac{2}{4} = \frac{1}{2}
\]
\[
x = \frac{-7 - 9}{4} = \frac{-16}{4} = -4
\]

Thus, the x-intercepts are \( \left( \frac{1}{2}, 0 \right) \) and \( (-4, 0) \).

#### 2.2. Y-intercept
The y-intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into \( f(x) \):

\[
f(0) = 2(0)^2 + 7(0) - 4 = -4
\]

So, the y-intercept is \( (0, -4) \).

---

### Summary of Intercepts

1. \( f(x) = -5x - 9 \):
   - X-intercept: \( \left( -\frac{9}{5}, 0 \right) \)
   - Y-intercept: \( (0, -9) \)

2. \( f(x) = 2x^2 + 7x - 4 \):
   - X-intercepts: \( \left( \frac{1}{2}, 0 \right) \) and \( (-4, 0) \)
   - Y-intercept: \( (0, -4) \)

Would you like me to sketch the graph for these functions or provide further explanations?

### Additional Questions:
1. How does the slope of the linear function \( f(x) = -5x - 9 \) affect its steepness?
2. How do the x-intercepts of the quadratic function influence its graph?
3. Can you determine the vertex of the quadratic function \( f(x) = 2x^2 + 7x - 4 \)?
4. What does the y-intercept represent in both functions?
5. How would these graphs behave for large positive and negative values of \( x \)?

**Tip**: When solving quadratic equations, always check if factoring is an option before using the quadratic formula.

Create a table of values with at least A points. Determine the x- and y-intercepts. Then sketch the graph. 1) f(x) = -5x - 9 2) f(x) = 2x^2 + 7x - 4

Learn how to determine the x- and y-intercepts for the linear function f(x) = -5x - 9 and the quadratic function f(x) = 2x^2 + 7x - 4. Follow a step-by-step solution using the intercept theorem and quadratic formula. Suitable for Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation