Question

I need the explanation to understand please y= 5x^2 + 1A.) Identify the coefficients (a, b, and c) B.) Tell whether the graph opens up or opens down C.) Find the vertex. Write as a coordinate. D.) Find the axis of symmetry. Write as an equation. E.) Find the y-intercept Write as a coordinate.

Answer 1

We need to remember the quadratic function in it's standard form:

`y=ax^2+bx+c`

where a,b,c can be any real number.

For the point A) We can compare this equation to the equation that they give us in the question,since the term with the quatratic x is 5x^2 we conclude that a=5, since there is no a linear term x in the equation we conclude that b=0, and finally since the independent term is 1, we conclude that c=1.

For the point B) The graph opens up because a=5 that is a positive number.

For the point c) The vertex is (0,1) because -b/2a=-0/10=0 and when we replace it in the equation we will obtain that y=1

For the point D) The axis of symmetry is the y-axis because there are no quadratic terms in the equation that involves the variable y. the equation of the axis of symmetry is x=0

For the point E) in accordance with the procedure of point C) the y- intercept will be (0,1)

the graph of the equation is: