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

Step-by-step 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=-(b)/(2a)`
`\mathrm{The\:parabola\:params\:are:}`
`a=1,\:b=-7,\:c=10`
`x_v=-(b)/(2a)`
`x_v=-(\left(-7\right))/(2\cdot \:1)`

Simplify:

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