Algebra 2 help . Use y = x2-8x+7?
Use y = x2-8x+7
a. What is the value of the discriminant?
b. What types of roots will this equation have? Ex: two complex roots, one repeated root, two real rational roots or two real irrational roots?
c. Find the roots by factoring and solving.
d. Find the roots by using the quadratic equation.
f. Find the y-intercept.
g. Complete the square, and write that form of the equation.
h. Find the vertex of the parabola.
i. Can you think of a reason why this equation could not possibly be the equation of the curve you printed?
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y = x² - 8x + 7
Tha'ts a quadratic function in the form y = ax² + bx + c, where a = 1, b = -8, c = 7.
a. The discriminant is represented by Δ.
Δ = b² - 4ac = (-8)² - 4(1)(7) = 64 - 28 = 36
b. The discriminant tells you the type of roots. If Δ is negative, the equation has two complex root. If Δ is zero, the equation has one repeated root (also called a double root). If Δ is positive, the equation has two real and distinct roots. For real and distinct roots, if Δ is a perfect square (like 1, 4, 9, 16, etc) then the real roots are rational; otherwise they are irrational.
For this equation Δ = 36. So there are two real and rational roots.
c. The roots occur wher y = 0, so
y = 0 = x² - 8x + 7
(x - 1)(x - 7) = 0
x = 1, x = 7 are the roots
d. x = (-b ± √Δ)/2a = (8 ± √36)/2
x = (8 + 6)/2 = 14/2 = 7
x = (8 - 6)/2 = 2/2 = 1
f. The y-intercept occurs at x = 0
y = x² - 8x + 7 = (0)² - 8(0) + 7 = 7
g. y = x² - 8x + 7
y = (x² - 8x + ___ ) + ___+ 7
y = (x² - 8x + 16) - 16 + 7 = (x - 4)² - 9
h. Completing the square form is the same as vertex form. Change the sign for the number in parentheses to get the x-coordinate. The y-coordinate is the number outside the parentheses just as it is. The vertex is (4, -9).
b. it will have two real roots because just use the vertex -b/2a and if it goes below the x axis it will tell you whethere it has real or nonreal solutions
d..quadratic formula you'll end up with two real rational zeros of (1,0) and (7,0) as the x-intercepts
f. yint is just the (0,7) from the last number of the equation
h. -b/2a = 8/2 = 4> take that four and plug it into x > 16-32+7=-9 so the vertex is (4,-9)
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