Question

The equation of a parabola is given. y=34x2−6x+15

Answer 1

The x coordinate of the vertex = -b/2a  = -(-6) / 2*34  = 0.08824

y coordinate = 34(0.08824^2 - 6(0.08824) + 15 =  14.735

so its (0.088, 14.735)     correct to 3 decimal places

Answer 2

Answer:

A quadratic equation is in the form of  $y=ax^2+bx+c$,....[1] then the axis of symmetry is given by:

$x = -\frac{b}{2a}$

Vertex of the function is given by:

$\text{vertex} = (-\frac{b}{2a}, f(-\frac{b}{2a}))$

As per the statement:

Given the function:

$y=f(x)=34x^2-6x+15$        ....[2]

Compare this with equation [1] we have;

a = 34 and b = -6

then;

$x = -\frac{-6}{2(34)}$

⇒$x =\frac{6}{68}=0.088252941$

⇒x =0.08825294

Substitute the value of x in [2] we have;

$f(0.08825294)=34(0.08825294)^2-6(0.08825294)+15$

$f(0.08825294)=0.264705882-0.529411765+15$

Simplify:

$f(0.08825294)=14.7352941$

⇒Vertex = (0.08825294,14.7352941)

Therefore, the coordinate of the vertex of the parabola is, (0.08825294,14.7352941)