The y-intercept is the point where it crosses the y axis so x would 0. So putting in 0 for x: y = x^2 - 8x + 7 y = 0^2 - 8(0) + 7 y = 0 - 0 + 7 y = 7 The y intercept is at the point (0,7).
b) The zeroes are the points where it crosses the x axis so it’s when the y is set to 0.
0 = x^2 - 8x + 7 Since it’s a quadratic equation we have to factor it. We fill in 2 numbers that add to -8 and multiplied to equal 7. (x +____)(x+ ____)
The 2 numbers are 7 and -1 because -1*-7=7 and -7+(-1)=-8. So: 0 = (x-7)(x-1)
So now we have x-7 and x-1 equaling some quantity. If either of those happens to equal zero, it makes the whole equation 0, because (x-7)0=0 and 0(x-1)=0
So we can set each of it separately to 0 to solve for x. x-7=0 x= 7
x-1=0 x= 1
The zeroes are at the points (1, 0) and (7, 0)
C. The Vertex Form of a Quadratic is: y = a(x-h)^2 + k. And the vertex is (h, k)
y = x^2 - 8x + 7 y - 7 = x^2 - 8x
We want to complete the square by adding some number to both sides of the equation so that when we factor it we are going to get (x-a)(x-a).
So take half of 8 to get two equal numbers that would be our “a”. 8/2=4 so we want (x - 4)(x- 4).
(x-4)(x-4) multiplies out to x^2 - 8 + 16.
continuing, y - 7 = x^2 - 8x
Add 16 to both sides. y - 7 + 16 = x^2 - 8x + 16
y + 9 = (x-4)(x-4) y + 9 = (x-4)^2 y = (x-4)^2 - 9 is the vertex form.
The vertex is at the point (4, -9). So the axis of symmetry is at the line x = 4.
D. The vertex is solved in C as the point (-4, -9).
4d + 12 = 4(d + 3) Basically, you just need to determine what 4d and 12 have in common. In this case, they both divide evenly by 4. Therefore 4 (d + 3) = 4d + 12 according to the distributive property.
