Grade 9 Algebra 1, Please Help!

Question

1.The function f is given by f(x) = x^2−2x. Which statement is true about the graph of f?

The graph has a y-intercept at (2,0).

The coordinates of the vertex are (1,1).

The graph of the function opens downward.

The x-intercepts are at (0,0) and (2,0).

2.A quadratic function f is given by f(x)=ax^2 + bx + c where a is not 0. Select all the statements that must be true about the graph of f.

A.The y-intercept of the graph is at (0,c).

B.The graph has an x-intercept at (c,0).

C.When a<0 the graph opens downward.

D.The graph has two x-intercepts.

E.If b=0, then the vertex is on the y-axis.

Answer 1

x^2 -2x = x(x-2) set each factor = 0 and solve for x to find the x intercepts 0 and 2 or the points (0,0) and (2,0)

the y intercept is 0 or (0,0)

the vertex is (1,-1), not (1,1)

It's an upward opening parabola, not downward

all statements are false, except the last on the x intercepts

2 A is True: y intercept is (0,c)

B is false: x intercepts are when y=0 and the quadratic formula gives the x intercepts

x = -b/2a + and - (1/2a)sqr(b^2 -4ac), which is not (c,0) although the y coordinate is correct

when a<0, the parabola opens downward, C is true

D is false. the quadratic may have 2, 1, or 0 x intercepts. If the discriminant <0, there are no real solutions, and the graph never intersects the x axis. If the discriminant = 0, there is one solution, and the graph doesn't "intersect" the x axis, but is tangent to it at one x value

E True: if b = 0, the axis of symmetry is x=0 and the vertex has an x coordinate = 0, so the vertex is on the y axis

A,C, E are True

B,D are False

ACE yes, BD no