# How to do question 8?

Feb 12, 2018

$a = \frac{3}{16}$, $h = - 2$, $k = 3$

#### Explanation:

It appears that by turning point it means that $\left(- 2 , 3\right)$ is the vertex and hence asthe equation $y = a {\left(x - h\right)}^{4} + k$ is in vertex form, where $\left(h , k\right)$ is vertex, we have the equation as

$y = a {\left(x - \left(- 2\right)\right)}^{4} + 3$ or $y = a {\left(x + 2\right)}^{4} + 3$

Now, it passes through point $\left(0 , - 6\right)$ hence

$6 = a {\left(0 + 2\right)}^{4} + 3$ or $6 = 16 a + 3$ i.e. $a = \frac{3}{16}$

Hence, equation is $y = \frac{3}{16} {\left(x + 2\right)}^{4} + 3$

i.e. $a = \frac{3}{16}$, $h = - 2$, $k = 3$ and graph appears as

graph{3/16(x+2)^4+3 [-12.67, 7.33, -0.96, 9.04]}