Write the equation of the parabola with:
Vertex $(- 3, 6)$ and $y$ -intercept -10

Answer

Expert–verified

Hide Steps

Answer

$y = - \frac{16}{9} (x + 3)^{2} + 6$

Steps

Step 1 ：Given the vertex of the parabola is $(- 3, 6)$ , we can substitute $h = - 3$ and $k = 6$ into the vertex form of a parabola equation: $y = a (x - h)^{2} + k$

Step 2 ： $y = a (x + 3)^{2} + 6$

Step 3 ：Use the given $y$ -intercept -10, which means $x = 0$ , and substitute these values into the equation:

Step 4 ： $- 10 = a (0 + 3)^{2} + 6$

Step 5 ：Solve for $a$ :

Step 6 ： $a = - \frac{16}{9}$

Step 7 ：Substitute the value of $a$ back into the equation:

Step 8 ： $y = - \frac{16}{9} (x + 3)^{2} + 6$

Write the equation of the parabola with:Vertex (−3,6) and y-intercept -10

Answer

Popular Problems

Write the equation of the parabola with:
Vertex $(- 3, 6)$ and $y$ -intercept -10