Question Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an $$ (x, y) $$ point. $$ y=5 x^{2}-70 x+230 $$ Answer

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The vertex of a parabola given by $$ y = ax^2 + bx + c $$ can be found using the formula for the $$ x $$-coordinate of the vertex:

$$
x = -\frac{b}{2a}
$$

For the equation

$$
y = 5x^2 - 70x + 230,
$$

the coefficients are $$ a = 5 $$ and $$ b = -70 $$.

1. Calculate the $$ x $$-coordinate:

$$
x = -\frac{-70}{2 \cdot 5} = \frac{70}{10} = 7
$$

2. Substitute $$ x = 7 $$ back into the equation to find the $$ y $$-coordinate:

$$
y = 5(7)^2 - 70(7) + 230
$$

$$
y = 5(49) - 490 + 230
$$

$$
y = 245 - 490 + 230
$$

$$
y = -15
$$

Thus, the vertex of the parabola is:

$$
(7, -15)
$$
The vertex of the parabola is at $$ (7, -15) $$.

Question Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an \( (x, y) \) point. \[ y=5 x^{2}-70 x+230 \] Answer

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