Question
The value of c in the standard form of the quadratic function y = ax2+bx+c
is
Question 8
6.
In the xy-coordinate plane, the graph of the equations y = 3x2 −12x −36
has zeros at x = FREE Cherry Blossom Flower Clipart | Pearly Arts and x =Tulip Clipart Images | Free Download | PNG Transparent ...,
where FREE Cherry Blossom Flower Clipart | Pearly Arts< Tulip Clipart Images | Free Download | PNG Transparent ....
The graph has a minimum at ( Four Leaf Clover Outline Images – Browse 9,367 Stock Photos ..., -48).
(3 points)
What are the values of
FREE Cherry Blossom Flower Clipart | Pearly Arts=
Tulip Clipart Images | Free Download | PNG Transparent ... =
and
Four Leaf Clover Outline Images – Browse 9,367 Stock Photos ... =
Answers
GPT-4o mini
To find the zeros and the vertex of the quadratic function \( y = 3x^2 - 12x - 36 \), we can follow these steps:
1. **Identify coefficients**: Here, \( a = 3 \), \( b = -12 \), and \( c = -36 \).
2. **Find the zeros**:
We can find the zeros of the function by using the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Substitute \( a \), \( b \), and \( c \) into the formula:
\[
x = \frac{-(-12) \pm \sqrt{(-12)^2 - 4(3)(-36)}}{2(3)}
\]
\[
x = \frac{12 \pm \sqrt{144 + 432}}{6}
\]
\[
x = \frac{12 \pm \sqrt{576}}{6}
\]
\[
x = \frac{12 \pm 24}{6}
\]
This gives us two solutions:
\[
x = \frac{36}{6} = 6 \quad \text{and} \quad x = \frac{-12}{6} = -2
\]
Thus, the zeros are:
- \( x = 6 \)
- \( x = -2 \)
3. **Find the vertex**:
The x-coordinate of the vertex for a quadratic function is given by the formula:
\[
x = -\frac{b}{2a}
\]
Substituting the values of \( b \) and \( a \):
\[
x = -\frac{-12}{2 \cdot 3} = \frac{12}{6} = 2
\]
To find the y-coordinate of the vertex, substitute \( x = 2 \) back into the equation:
\[
y = 3(2)^2 - 12(2) - 36
\]
\[
y = 3(4) - 24 - 36
\]
\[
y = 12 - 24 - 36 = -48
\]
Thus, the vertex is at \( (2, -48) \).
4. **Conclusion**:
- \( FREE \, Cherry \, Blossom \, Flower \, Clipart \, | \, Pearly \, Arts = -2 \)
- \( Tulip \, Clipart \, Images \, | \, Free \, Download \, | \, PNG \, Transparent = 6 \)
- \( Four \, Leaf \, Clover \, Outline \, Images \, - \, Browse \, 9,367 \, Stock \, Photos \, .. = -48 \)
These values correspond to the zeros of the quadratic function and the y-coordinate of the vertex.
1. **Identify coefficients**: Here, \( a = 3 \), \( b = -12 \), and \( c = -36 \).
2. **Find the zeros**:
We can find the zeros of the function by using the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Substitute \( a \), \( b \), and \( c \) into the formula:
\[
x = \frac{-(-12) \pm \sqrt{(-12)^2 - 4(3)(-36)}}{2(3)}
\]
\[
x = \frac{12 \pm \sqrt{144 + 432}}{6}
\]
\[
x = \frac{12 \pm \sqrt{576}}{6}
\]
\[
x = \frac{12 \pm 24}{6}
\]
This gives us two solutions:
\[
x = \frac{36}{6} = 6 \quad \text{and} \quad x = \frac{-12}{6} = -2
\]
Thus, the zeros are:
- \( x = 6 \)
- \( x = -2 \)
3. **Find the vertex**:
The x-coordinate of the vertex for a quadratic function is given by the formula:
\[
x = -\frac{b}{2a}
\]
Substituting the values of \( b \) and \( a \):
\[
x = -\frac{-12}{2 \cdot 3} = \frac{12}{6} = 2
\]
To find the y-coordinate of the vertex, substitute \( x = 2 \) back into the equation:
\[
y = 3(2)^2 - 12(2) - 36
\]
\[
y = 3(4) - 24 - 36
\]
\[
y = 12 - 24 - 36 = -48
\]
Thus, the vertex is at \( (2, -48) \).
4. **Conclusion**:
- \( FREE \, Cherry \, Blossom \, Flower \, Clipart \, | \, Pearly \, Arts = -2 \)
- \( Tulip \, Clipart \, Images \, | \, Free \, Download \, | \, PNG \, Transparent = 6 \)
- \( Four \, Leaf \, Clover \, Outline \, Images \, - \, Browse \, 9,367 \, Stock \, Photos \, .. = -48 \)
These values correspond to the zeros of the quadratic function and the y-coordinate of the vertex.