. Given the function f(x)=5x^2+10x-15 convert it to vertex and factored form, and list the key properties of the function, and then graph it (graph paper on next page) [16]

Question

Answer 1

### Vertex Form:

### Factored Form:

### Key Properties:- Vertex:

- Axis of Symmetry:

- X-intercepts:

and

- Y-intercept:

Answer 2

## Step 1: Convert to Vertex Form### To convert the quadratic function

to vertex form, we complete the square. The vertex form of a quadratic function is given by

, where

is the vertex of the parabola.Given:

First, factor out the coefficient of

from the first two terms:

Next, complete the square inside the parentheses:

Add and subtract

inside the parentheses:

Now substitute back into the function:

Thus, the vertex form is:

## Step 2: Convert to Factored Form### To convert the quadratic function to factored form, we find the roots of the equation by solving

.Using the quadratic formula:

where

,

, and

:

So the roots are:

Thus, the factored form is:

## Step 3: List Key Properties### The key properties of the function

are as follows:- **Vertex**:

- **Axis of Symmetry**:

- **X-intercepts**:

and

- **Y-intercept**:

Question