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

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Answer

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

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

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

Answer

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