# How do I find the vertex, axis of symmetry, y-intercept, x-intercept, domain and range of f(x) = −4(x − 8)^2 + 3?

##### 1 Answer
Oct 8, 2015

vertex is (8,3). Axis of symmetry is x=8. x intercepts are $8 \pm \frac{\sqrt{3}}{2}$ . y intercept is (0, -253). Domain $\left\{x : x \in \mathbb{R} , - \infty \le x \le + \infty\right\}$. Range is $\left\{y : y \in \mathbb{R} , 3 \ge y \ge - \infty\right\}$

#### Explanation:

The given equation is already given in vertex form. The figure is an vertical parabola, opening down ward. The vertex is (8,3), axis of symmetry is x-8=0 that is x=8. In the given equation put, x=0 to obtain y= -253. Hence y- intercept is (0, -253). For x intercepts put f(x)=0 and solve for x to get x= $8 \pm \frac{\sqrt{3}}{2}$

domain is whole of real numbers as x can have any real value.
Domain $\left\{x : x \in \mathbb{R} , - \infty \le x \le + \infty\right\}$. Range is $\left\{y : y \in \mathbb{R} , 3 \ge y \ge - \infty\right\}$