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# The graph of y=ax^2+bx+x is given below, where a,b , and c are integers. Find a+b+c.

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The graph of y=ax^2+bx+x is given below, where a,b , and c are integers. Find a+b+c.

Jan 6, 2019

#1
+103689
+2

The graph of y=ax^2+bx+x is given below, where a,b , and c are integers. Find a+b+c.

I assume that is meant to be

The graph of y=ax^2+bx+c is given below, where a,b , and c are integers. Find a+b+c.

parabola

axis of symmetry is x=1

so

$$\frac{-b}{2a}=1\\ b=-2a$$

so we have

$$y=ax^2-2ax+c$$

When x=0 y=1 so   c=1

$$y=ax^2-2ax+1$$

When x=1, y=3

so

$$y=ax^2-2ax+1\\ 3=a-2a+1\\ 2=-a\\ a=-2$$

$$\boxed{y=-2x^2+4x+1}$$

.
Jan 7, 2019

#1
+103689
+2

The graph of y=ax^2+bx+x is given below, where a,b , and c are integers. Find a+b+c.

I assume that is meant to be

The graph of y=ax^2+bx+c is given below, where a,b , and c are integers. Find a+b+c.

parabola

axis of symmetry is x=1

so

$$\frac{-b}{2a}=1\\ b=-2a$$

so we have

$$y=ax^2-2ax+c$$

When x=0 y=1 so   c=1

$$y=ax^2-2ax+1$$

When x=1, y=3

so

$$y=ax^2-2ax+1\\ 3=a-2a+1\\ 2=-a\\ a=-2$$

$$\boxed{y=-2x^2+4x+1}$$

Melody Jan 7, 2019