📌 Quadratic = U-shaped parabola. Graph A shows a parabola. Graph B is a straight line → linear, not quadratic.
Question 2 of 10
Florida standards 5A-5CHard Calc
Solve: 3x+4y=10, 2x−4y=−5
A(0, 2.5)
B(2, 1)
C(1, 1.75)
D(1, 2)
Explanation
📌 Add: 5x=5 → x=1. 3(1)+4y=10 → 4y=7 → y=7/4=1.75
Question 3 of 10
Florida standards 8A-8BMedium Calc Diagram
For a quadratic equation ax² + bx + c = 0, the discriminant is b² − 4ac. It tells us how many times the related parabola y = ax² + bx + c crosses the x-axis — and therefore how many real solutions the equation has.
The discriminant's sign matches the number of x-axis crossings.
Which statement about D = 0 is TRUE?
ATwo real solutions — the parabola crosses the x-axis twice
BNo real solutions — the parabola doesn't reach the x-axis
CExactly one real solution — the parabola is tangent to the x-axis
DThe number of solutions can't be determined from D alone
Explanation
The discriminant b² − 4ac counts how many real solutions a quadratic equation has by reflecting how many times the parabola y = ax² + bx + c crosses the x-axis.
The three cases: • D > 0: parabola crosses the x-axis at TWO different points → 2 real solutions. • D = 0: parabola is *tangent* to the x-axis — it touches at exactly ONE point (the vertex itself sits on the x-axis) → 1 real solution (often called a *double root*). • D < 0: parabola sits entirely above or below the x-axis, never touching it → 0 real solutions (the roots are complex / imaginary).
Application: D = 0 is the borderline case useful for problems like "for what value of c does ax² + bx + c = 0 have exactly one solution?" — set b² − 4ac = 0 and solve.
Question 4 of 10
Florida standards 5A-5CMedium Calc Word Diagram
The system of equations is graphed below. How many solutions does it have?
AOne solution
BInfinitely many solutions
CNo solution
DTwo solutions
Explanation
📌 The lines are parallel (same slope, different y-intercepts). Parallel lines NEVER intersect → NO solution.
Systems with no solution are called 'inconsistent.'
Question 5 of 10
Florida standards 6A-6CMedium Calc Word
Use the quadratic formula for x² − 4x + 3 = 0
Ax = −1, −3
Bx = 1, 3
Cx = 0, 4
Dx = 2, 4
Explanation
📌 a=1, b=−4, c=3. x = (4 ± √(16−12))/2 = (4±2)/2 → x=3 or x=1
Question 6 of 10
Florida standards 5A-5CHard Calc Word
Solve: 2x + 3y = 13, 4x − y = 5
A(2, 3)
B(1, 4)
C(3, 2)
D(4, 1)
Explanation
📌 From eq2: y = 4x − 5 Substitute: 2x + 3(4x−5) = 13 → 2x + 12x − 15 = 13 → 14x = 28 → x = 2 y = 4(2) − 5 = 3
Question 7 of 10
Florida standards 5A-5CMedium Calc Word Diagram
The graph shows two lines. What is the solution to the system?
A(3, 0)
B(1, 2)
C(2, 3)
D(0, 1)
Explanation
📌 The solution is where the lines intersect = (1, 2). Verify: y = x + 1 → 2 = 1 + 1 ✓ y = −x + 3 → 2 = −1 + 3 ✓
Question 8 of 10
Florida standards 6A-6CMedium Calc Word Diagram
The parabola in the graph below has a vertex at which point?
A(0, 0)
B(-1, 2)
C(2, 1)
D(1, -2)
Explanation
The vertex is the lowest point of an upward-opening parabola, marked at approximately (1, -2).
Question 9 of 10
Florida standards 6A-6CHard Calc Word
Complete the square: x² + 6x + ___ = (x + ___)²
A6, 3
B3, 9
C9, 3
D36, 6
Explanation
📌 Half of 6 = 3. Square it = 9. x² + 6x + 9 = (x + 3)²
Question 10 of 10
Florida standards 1A-1GEasy Calc Word Diagram
A cell phone plan charges $30 per month plus $0.10 per text. Which equation represents the monthly cost C for t texts?
AC = 0.10(30 + t)
BC = 30 + 0.10t
CC = 30.10t
DC = 30t + 0.10
Explanation
📌 Fixed cost = $30 (base monthly charge) Variable cost = $0.10 per text = 0.10t Total: C = 30 + 0.10t
💡 This is a linear equation in slope-intercept form: y = mx + b where m = 0.10 and b = 30.