Answer:
[tex]( - 0.5 , - 4.5 )[/tex]
Step-by-step explanation:
Rewrite the equation in vertex form.
Complete the square for
[tex]2 {x}^{2} + 2x - 4[/tex]
Use the form
[tex]a {x}^{2} + bx + c[/tex]
to find the values of a, b, and c.
a = 2
b = 2
c = −4
Consider the vertex form of a parabola.
[tex]a(x + d) ^{2} + e[/tex]
Find the value of d using the formula
[tex]d = \frac{b}{2a} [/tex]
[tex]d = \frac{1}{2} [/tex]
Find the value of e using the formula
[tex]e = c - \frac{ {b}^{2} }{4a} [/tex]
[tex]e = - \frac{9}{2} [/tex]
Substitute the values of a, d, and e into the vertex form
[tex]2(x + \frac{1}{2} ) ^{2} - \frac{9}{2} [/tex]
Set y equal to the new right side.
[tex]y = {2(x + \frac{1}{2}) }^{2} - \frac{9}{2} [/tex]
Use the vertex form,
[tex]y = a(x - h) ^{2} + k[/tex]
to determine the values of a, h, and k.
a = 2
h = -1/2
k = -9/2
Find the vertex (h,k).
[tex]( - \frac{1}{2} , - \frac{9}{2} )[/tex]
