The vertex form of the quadratic equation is y = (9/4)*(x + 2/3)² - 2
How to write the quadratic equation in vertex form?
We want to rewrite the quadratic equation:
y = (9/4)*x² + 3x - 1
Remember that for a general quadratic:
y = ax² + bx + c
The vertex is at:
x = -b/2a
So in our case, the vertex is at:
y = (9/4)*x² + 3x - 1
x = -3/(2*9/4)
x = -3/(9/2)
x = -6/9 = -2/3
Evaluating there, we will get:
y = (9/4)*(-2/3)² + 3*(-2/3) - 1
y = -2
Then the vertex is at (-2/3, -2) and the leading coefficient is (9/4), then we can write:
y = (9/4)*(x + 2/3)² - 2