Скачать или смотреть Standard to Vertex Form Steps with 4 Examples and General Solution

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Standard to Vertex Form
Standard Form: y=ax^2+bx+c
Vertex Form: y=a(x-h)^2+k
Perfect Square: (x±h)^2=x^2±2xh+h^2
Maximum and Minimum from Vertex Form
Steps to Convert Standard to Vertex Form
y=ax^2+bx+c
y=a[x^2+b/a x]+c
y=a[x^2+b/a x+(b/2a)^2-(b/2a)^2 ]+c
y=a[(x+b/2a)^2-(b/2a)^2 ]+c
y=a[(x+b/2a)^2-b^2/(4a^2 )]+c
y=a(x+b/2a)^2-b^2/4a+c
y=a(x+b/2a)^2+(〖-b〗^2+4ac)/4a
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Quadratic Function Exam Review:
Q1. Simplify: and
Q2. For what value of k does the equation y 5x2 + 6x + k have each number of roots?

a. Two real roots b. One real root c. No real root

Q3. Factor: 2x3 – 8x2 – 42x and (3a + 1)2 – (a – 1)2

Q4. Solve the equation: 3x2 – 13x – 10 = 0

Q5. Solve the equation:

Q6. Graph y = 2x2 + 16x + 31

Q7. Determine the x-intercept of y = -0.5(x + 4)2 + 2

Q8. Express y = -3(x + 3)2 + 75 in factored form.

Q9. Parabola has a y-intercept of -4 and pass through the points (-2, 8) and (1, -1). Determine the vertex of the parabola.

Q10. What value of c will make the expression x2 – 8x + c a perfect square?
Find the vertex and the y-intercept to get the equation of the parabola in vertex form.