We're reviewing and I forgot how to do this.

Given y=x2-4+3 (x2 is x squared)

a)write in standard from
b)find vertex
c)find equation of the axis of symmetry
d)find the x-intercepts
e)find the y-intercept

a) standard form is the simplest version of the equation. so the standard form would be x^2-1. (-4+3= -1)

b) because this is a parabola, the vertex if the lowest or highest point on the graph. Put the equation into your calculator and (2nd)(trace)maximum or minimum to find the answer. in this case you would use minimum. (0,-1)
C) in this case, the axis of symmetry equation is x=0
d) in order to fin the x intercepts, you can go put y=0 into your calculator as y2 and (2nd)(trace)(5)-intersect- to find the two zeros you will get.
e) in y=mx+b equations, your y intercept is b.

No problem! Let's go step by step to answer each part of the question.

a) To write the given equation in standard form, we need to rearrange it to the form of y = ax^2 + bx + c.

Given the equation y = x^2 - 4x + 3, it is already in standard form.

b) To find the vertex of the parabola, we can use the formula: x = -b / (2a) and substitute the values of a and b from the equation. In this case, a = 1 and b = -4.

x = -(-4) / (2*1) = 4 / 2 = 2.

So, the x-coordinate of the vertex is x = 2. To find the y-coordinate, substitute x = 2 into the equation:

y = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1.

Therefore, the vertex is (2, -1).

c) The equation of the axis of symmetry is given by the formula: x = -b / (2a), which is the x-coordinate of the vertex. In this case, the axis of symmetry is x = 2.

d) To find the x-intercepts, we need to solve the quadratic equation when y = 0. So, we substitute y = 0 into the equation:

0 = x^2 - 4x + 3.

To solve this, you can use factoring, completing the square, or the quadratic formula. In this case, let's use factoring:

0 = (x - 3)(x - 1).

Setting each factor equal to zero, we get x - 3 = 0 and x - 1 = 0.
Solving these equations, we find x = 3 and x = 1.

Therefore, the x-intercepts are (3, 0) and (1, 0).

e) To find the y-intercept, we substitute x = 0 into the equation:

y = (0)^2 - 4(0) + 3 = 0 - 0 + 3 = 3.

Hence, the y-intercept is (0, 3).

So, to summarize:

a) The equation is already in standard form: y = x^2 - 4x + 3.
b) The vertex is (2, -1).
c) The equation of the axis of symmetry is x = 2.
d) The x-intercepts are (3, 0) and (1, 0).
e) The y-intercept is (0, 3).

I hope this explanation helps you with your review! Let me know if you have any further questions.