- a x ^ 2 - b x - c = - ( a x ^ 2 + b x + c )
Quadratic function can be concave up or concave down.
If a x ^ 2 + b x + c concave up or concave down graph of - a x ^ 2 - b x - c will be concave down or concave up.
The graph is rotated 180 ° around the x - axis, but x-intercepts stay same.
So x-intercepts of - a x ^ 2 - b x - c = x-intercepts of a x ^ 2 + b x + c
( m , 0 ) , ( n , 0 )
The graph of a quadratic function can have 0, 1 or 2 x-intercepts. How can you predict the number of x-intercepts without drawing the graph or (completely) solving the related equation?
Suppose that the graph of f(x) = ax^2+bx+c has x-intercepts (m,0) and (n,0). What are the x-intercepts of g(x) = –ax^2–bx–c?
4 answers
How can you predict the number of x-intercepts without drawing the graph.
Discriminant = b ^ 2 - 4 a c
If the discriminant is positive, then there are two distinct roots ( x - intercepts ).
If the discriminant is zero, then there is exactly one real root x - intercept ).
If the discriminant is negative, then there are no real roots( no one x - intercepts ).
Discriminant = b ^ 2 - 4 a c
If the discriminant is positive, then there are two distinct roots ( x - intercepts ).
If the discriminant is zero, then there is exactly one real root x - intercept ).
If the discriminant is negative, then there are no real roots( no one x - intercepts ).
x intercepts -3,1 points on the graph (
2,2.5)
2,2.5)
Which of the following illustration a quadratic function?
|. g(x)=2 - x²
||. f(X) =6x-4+3×3
|||. y=2ײ -3 x +5
IV. C(x)=x(x-2)+2r²
|. g(x)=2 - x²
||. f(X) =6x-4+3×3
|||. y=2ײ -3 x +5
IV. C(x)=x(x-2)+2r²
1 answer