Question

EXTREMELY desperate for help spending lots of points on this
can someone help me with the file attached?
And
https://brainly.com/question/27140824
just 2 questions

Answer 1

Answer:

Factored form:

$y=\left(-\dfrac14x+\dfrac12 \right)(x-4)$

Standard form:

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

when x = 1, $y=-\dfrac34$

Step-by-step explanation:

Part (a)

The zeros are where the curve intersects the x-axis (where y = 0)

From inspection of the graph, the points of intersection with the x-axis are (2, 0) and (4, 0)

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

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

Therefore, we can write the equation as:

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

(where a is some constant to be determined)

The y-intercept is when x=0 .

From inspection of the graph, the point of intersection with the y-axis is (0, -2)

Therefore, substitute x = 0 into the equation, set it to -2 and solve for a:

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

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

$\implies 8a=-2$

$\implies a=-\dfrac14$

Therefore, the final equation of the parabola is:

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

$\implies y=\left(-\dfrac14x+\dfrac12 \right)(x-4)$

Standard form of a quadratic equation:  $y=ax^2+bx+c$

To express the equation in standard form, simply expand:

$\implies y=-\dfrac14x^2+x+\dfrac12x-2$

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

Part (b)

Substitute x = 1 into the equation and solve for y:

$\implies y=-\dfrac14(1)^2+\dfrac32(1)-2$

$\implies y=-\dfrac14+\dfrac32-2$

$\implies y=-\dfrac14+\dfrac64-\dfrac84$

$\implies y=-\dfrac34$