Question

Transform the quadratic equation from vertex form to standard form and state the axis of symmetry.

y=3(x+3)2−4


(1 point)
Responses

y=3x2+18x+23
and x=−3
y equals 3 x squared plus 18 x plus 23 and x equals negative 3

y=3x2+18x+23
and x=3
y equals 3 x squared plus 18 x plus 23 and x equals 3

y=3x2+18x+31
and x=−3
y equals 3 x squared plus 18 x plus 31 and x equals negative 3

y=x2+6x+5
and x=3
y equals x squared plus 6 x plus 5 and x equals 3

Answer 1

To transform the given quadratic equation from vertex form to standard form, let's start with the equation:

\[ y = 3(x + 3)^2 - 4. \]

1. **Expand the equation**:

First, expand \( (x + 3)^2 \):

\[ (x + 3)^2 = x^2 + 6x + 9. \]

Now substitute this back into the equation:

\[ y = 3(x^2 + 6x + 9) - 4. \]

2. **Distribute the 3**:

\[ y = 3x^2 + 18x + 27 - 4. \]

3. **Combine like terms**:

\[ y = 3x^2 + 18x + 23. \]

Now we have the quadratic in standard form:

\[ y = 3x^2 + 18x + 23. \]

Next, to find the axis of symmetry, we can use the vertex form. The vertex of the quadratic is at \( x = h \), where \( h \) is from the vertex form \( y = a(x - h)^2 + k \). In our equation, \(-3\) is the value of \( h \) (since \( x + 3 \) can be rewritten as \( x - (-3) \)).

Thus, the axis of symmetry is:

\[ x = -3. \]

Finally, we summarize the results:

**Standard Form**: \( y = 3x^2 + 18x + 23 \)

**Axis of Symmetry**: \( x = -3 \)

So the correct response is:

**y=3x²+18x+23 and x=−3.**