What is the axis of symmetry and vertex for the graph #f(x)=4x^2-8x+3#?

Question

HIX Tutor · Accepted Answer

undefined To find the axis of symmetry and vertex of the graph $ f(x) = 4x^2 - 8x + 3 $, follow these steps:

### Step 1: Find the Axis of Symmetry
The formula for the axis of symmetry is:
$$
x = -\frac{b}{2a}
$$
Here, $ a = 4 $ and $ b = -8 $.

1. Plug in the values:
   $$
   x = -\frac{-8}{2 \times 4} = \frac{8}{8} = 1
   $$

### Step 2: Find the Vertex
Now we find the vertex using the x-value we just found.

1. Plug $ x = 1 $ back into the function:
   $$
   f(1) = 4(1)^2 - 8(1) + 3
   $$

2. Calculate:
   $$
   f(1) = 4(1) - 8 + 3 = 4 - 8 + 3 = -1
   $$

### Conclusion
So, the axis of symmetry is:
$$
x = 1
$$
And the vertex is:
$$
(1, -1)
$$

Eli Assouline · Answer

Vertex (1, -1)

x-coordinate of vertex and axis of symmetry: #x = -b/(2a) = 8/8 = 1# y-coordinate of vertex: y(1) = 4 - 8 + 3 = -1 Vertex (1, -1) graph{4x^2 - 8x + 3 [-5, 5, -2.5, 2.5]}

Eli Assouline · Answer

undefined The axis of symmetry is $x = 1$ and the vertex is $ (1, -1) $.