Put the quadratic equation y=4x^2-24x+5 into vertex form by completing the square then state the coordinates of the vertex.

(3, -31)

Step-by-step explanation:

Factor 4 out of the first two terms:

y=4x^2-24x+5 becomes y=4(x^2 - 6x) +5

Next, complete the square of (x^2 - 6x):  It is x^2 - 6x + 9 - 9

Insert this into y=4(x^2 - 6x) +5 in place of x^2 - 6x:

y=4(x^2 - 6x) +5 => y=4(x^2 - 6x + 9 - 9) +5, or

                                y=4( (x - 3)^2 - 9 ) + 5, or

                                y = 4(x - 3)^2 - 36 + 5, or:

                                 y = 4(x - 3)^2 - 31

Compare this to:       y = a(x - h)^2 + k

We see that the coordinates of the vertex (h, k) are (3, -31), and that a = 4.

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!

a

step-by-step explanation: