jaronmartinez
Answered

For all functions of the form f(x) = ax2 + bx + c, which is true when b = 0?


A.The graph will always have zero x-intercepts.

B.The function will always have a minimum.

C.The y-intercept will always be the vertex.

D.The axis of symmetry will always be positive.

Verified Answer :

apologiabiology

when b=0
f(x)=ax^2+c

test each
A. with x^2-1, A is false
B. with -x^2-1, B is false
C. cannot find contradiction
D. the axis is actually x=0, 0 is nithere positive nor negative, false


answer is C

lhannearaujo

The correct statement is the letter C - The y-intercept will always be the vertex.

Quadratic function

The quadratic function can be represented by a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

The vertex of an up-down facing parabola of the form ax²+bx+c is \(x=-\frac{b}{2a}\). Knowing the x-coordinate of vertex, you can find the y-coordinate of vertex. When a vertical line passes through the vertex of the parabola, it is called the axis of symmetry.

The y-intercept is the point where the function crosses the y-axis. And, the x-intercept is the point where the function crosses the x-axis, in other words, when y=0.

For b=0, from the formula for vertex:

\(x_v=-\frac{b}{2a}\\ \\ x_v=0\)

Thus, for \(x_v=0\) and b=0, you will have

\(y_v=a*(x_v)^2+bx+c\\ \\ y_v=a*(0)^2+0*x+c\\ \\ y_v=c\)

See a numerical example, for a=1, b=0 and c=-9 in the attached image.

Because the coefficient b=0, you have x-vertex=0 and y-vertex=c=-9.

Learn more about the vertex of the quadratic function here:

brainly.com/question/26203210

View image lhannearaujo

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