Intersections 25141

The quadratic function has the formula y = x²-2x-3. Sketch a graph of this function. Find the intersections with the axes. Find the vertex coordinates.

Correct answer:

y0 =  -3
x1 =  3
x2 =  -1
x3 =  1
y3 =  -4

Step-by-step explanation:

f(x) =  y=x22x3  x0=0 y0=x022 x03=3  Py = (0;y0) =(0;3)
y=0 0=x22 x3  0=x22 x3 x2+2x+3=0 x22x3=0  a=1;b=2;c=3 D=b24ac=2241(3)=16 D>0  x1,2=2ab±D=22±16 x1,2=22±4 x1,2=1±2 x1=3 x2=1  Px=(x1;0)=(3;0)

Our quadratic equation calculator calculates it.

x2=(1)=1  Px=(x2;0)=(1;0)
a=1 b=2 c=3  x3=b/(2 a)=(2)/(2 1)=1
y3=b2/(4 a)+c=(2)2/(4 1)+(3)=4  V(x3;y3)=(1;4)

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