What is the answer to y=4x(squared) - 4x - 3?

Question

how it is done, x/y intercepts, how to work out the turning point on a graph due to this equation. 

Answer 1

The equation y = 4x² - 4x - 3

The quadratic equation represent a parabola in the graph.

Compare it to y = ax² + bx + c

a = 4, b = - 4 and c = - 3

Find the value of y intercept of the equation by substituting x = 0.

y = 4(0)² - 4(0) - 3

y = - 3

y intercept is - 3.

 

Find the value of x intercept of the equation by substituting y = 0.

 4x² - 4x - 3 = 0

4x² - 6x + 2x - 3 = 0

2x(2x - 3) + 1(2x - 3) = 0

2x - 3 = 0 and 2x + 1 = 0

2x = 3 and 2x = - 1

x = 3/2 and x = -1/2

x intercepts are 3/2 and -1/2.

 

Turning point is vertex of the equation.

To find x coordinate of turning point  x = - b/2a.

x = - (- 4)/2(4) = 4/8

x = 1/2

To find y coordinate of turning point substitute x = 1/2 in y = 4x² - 4x - 3.

y = 4(1/2)² - 4(1/2) - 3

y = 1 - 2 - 3

y = - 4

Turning point (x , y) = (0.5, -4)