Question

is there absolutely anyone here that can help me with this? very desperate
either this link or this file?
absolutely any of the 2
https://brainly.com/question/27159839

Answer 1

Answer:

(a) Factored form:

 $y=-\dfrac14(x-2)(x-4)$

Standard form:

 $y=-\dfrac14x^2+\dfrac32x-2$

(b) $y=-\dfrac34$

Step-by-step explanation:

Part (a)

From inspection of the graph, it appears that the curve is a parabola that opens downwards.

The factored form of the quadratic equation that opens downwards is

$y=-a(x+b)(x+c)$

(when the parabola opens upwards, the leading coefficient is positive, and when the parabola opens downwards, the leading coefficient is negative)

We can see that the zeros (where the curve intercepts the x-axis) are at
x = 2 and x = 4

$\implies x = 2\implies x-2=0$

$\implies x=4 \implies x-4=0$

Therefore:

$y=-a(x-2)(x-4)$

We can see that the y-intercept is at (0, -2).  So to find $a$, substitute these values into the equation and solve:

$\implies -a(0-2)(0-4)=-2$

$\implies -a(-2)(-4)=-2$

$\implies -8a=-2$

$\implies a=\dfrac{-2}{-8}=\dfrac14$

Therefore, the equation of the curve in factored form is:

$y=-\dfrac14(x-2)(x-4)$

To convert to standard form, simply expand:

$y=-\dfrac14(x-2)(x-4)$

$\implies y=-\dfrac14(x^2-6x+8)$

$\implies y=-\dfrac14x^2+\dfrac32x-2$

Part (b)

To find the value of y when x = 1, simply substitute x = 1 into the equation (I have used the factored form, but you could also use the standard form of the final equation).

$\implies -\dfrac14(1-2)(1-4)=-\dfrac14(-1)(-3)=-\dfrac34$