Question

On a piece of paper, graph y = x2 - 7x + 10 and identify the y-intercept. Thendetermine which answer choice matches the graph that you drew andcorrectly identifies the y-intercept.A. y-Intercept: (0, -10)10 Y5-5-5B. y-Intercept: (0,10)10у5-5-5O C. y-Intercept: (0, -10),

Answer 1

EXPLANATION

We first can draw the vertex in order to obtain the minimum value:

$\mathrm{The\:vertex\:of\:an\:up-down\:facing\:parabola\:of\:the\:form}\:y=ax^2+bx+c\:\mathrm{is}\:x_v=-\frac{b}{2a}$$\mathrm{The\:parabola\:params\:are:}$$a=1,\:b=-7,\:c=10$$x_v=-\frac{b}{2a}$$x_v=-\frac{\left(-7\right)}{2\cdot \:1}$

Simplify:

$y_v=-\frac{9}{4}$$\mathrm{Therefore\:the\:parabola\:vertex\:is}$$\left(\frac{7}{2},\:-\frac{9}{4}\right)$

Now, we need to compute the intercepts:

Plug y=0 into the equation and solve the resulting equation 0=x^2-7x+10:

The x-intercept are the following:

(2,0) and (5,0)

Identifying the y-intercept:

Plug x=0 into the equation and solve the resulting equation y=10 for y:

$y=0^2-7*0+10$

Computing the power and multiplying terms:

$y=10$

The y-intercept is at (0,10)

In conclusin, the appropriate option is OPTION B