Question

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left parenthesis, x, comma, y, right parenthesis(x,y) point.
y, equals, 5, x, squared, plus, 20, x, plus, 35
y=5x
2
+20x+35

Answer 1

To find the vertex of the parabola given by the equation \( y = 5x^2 + 20x + 35 \), we can use the vertex formula for a quadratic function of the form \( y = ax^2 + bx + c \).

The x-coordinate of the vertex can be found using the formula:

\[
x = -\frac{b}{2a}
\]

In this equation:
- \( a = 5 \)
- \( b = 20 \)

Now, plugging in the values:

\[
x = -\frac{20}{2 \cdot 5} = -\frac{20}{10} = -2
\]

Next, we substitute \( x = -2 \) back into the equation to find the corresponding y-coordinate:

\[
y = 5(-2)^2 + 20(-2) + 35
\]
\[
y = 5(4) - 40 + 35
\]
\[
y = 20 - 40 + 35
\]
\[
y = 15
\]

So, the coordinates of the vertex of the parabola are:

\[
\boxed{(-2, 15)}
\]