factor y= 4𝑥^2 − 28𝑥 + 49
To factor the quadratic equation y = 4𝑥^2 − 28𝑥 + 49, we first observe that all the coefficients are positive. Therefore, we know that the quadratic equation does not have any real roots.
Using the quadratic formula, we have:
𝑥 = (−𝑏 ± √(𝑏^2 − 4𝑎𝑐))/(2𝑎)
Plugging in the values from the equation y = 4𝑥^2 − 28𝑥 + 49:
𝑥 = (−(−28) ± √((−28)^2 − 4(4)(49)))/(2(4))
= (28 ± √(784 − 784))/(8)
= (28 ± √(0))/(8)
= (28 ± 0)/(8)
= 28/8 = 7/2
This means that the quadratic equation has a double root at 𝑥 = 7/2.
Therefore, the factored form of the equation is:
y = 4(𝑥 − 7/2)^2