# How do you write f(x)= -x^2 + 3x + 10 in vertex form and identify the vertex, y intercept and x intercept?

Jul 4, 2015

$f \left(x\right) = - {x}^{2} + 3 x + 10$

#### Explanation:

x-cordinate of vertex: $x = \left(- \frac{b}{2} a\right) = - \frac{3}{-} 2 = \frac{3}{2}$
y-coordinate of vertex: $y = f \left(\frac{3}{2}\right) = - \frac{9}{4} + \frac{9}{2} + 10 = \frac{49}{4}$

Vertex form: $f \left(x\right) = - {\left(x - \frac{3}{2}\right)}^{2} + \frac{49}{4}$
To find y-intercept, make x = 0 --> y = 10
To find x-intercepts, solve f(x) = 0.
Find 2 numbers knowing sum (-3) and product (-10).
The 2 real roots (x-intercepts) are: -2 and 5.