Question

Draw the graph of the equation 4x²-6x+3 using the -2≤x≤3 use a scale of 2cm to 1unit on the x-axis, 1cm to 4units in the y-axis.
Find the graphfind;
(a) minimum value of y
(b) The roots of the equation 4x²-6x-3=0
(c) The value of x when y=5
(d) The solution set of the equation 4x²-6x-7=0
.

Please help please. I have plot the graph but I dbt know how to do the rest.

Answer 1

did you graph it?
It should be easy to answer some of the questions using the graph.

(a) look at the vertex.
4x^2-6x+3 = (2x-3/2)^2 + 3/4
(b) use the quadratic formula
(c) just solve 4x^2-6x+3=5
(d) again use the QF

Answer 2

Graphic solutions:

Use the graph.

a)

y = 4x²-6x+3

has its mimum value at :

xmin = 3 / 4

ymin = 3 / 4


b)

A vertical translation by 3 - ( - 3 ) = 3 + 3 = 6 units

Subtract 6 to each value of y.

The roots of the equation 4x²-6x-3=0

approx.

x = - 0.4 and x = 1.9


c)

y = 4x²-6x+3 = 5

approx.

x = - 0.3 and x = 1.8


d)

A vertical translation by 3 - ( - 7 ) = 3 + 7 = 10 units

Subtract 10 to each value of y.

The roots of the equation 4x²-6x-7=0

approx.

x = - 0.8 and x = 2.3